Tcl Library Source Code

[//000000001]: # (blowfish \- Blowfish Block Cipher)
[//000000002]: # (Generated from file 'blowfish\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2003, Pat Thoyts <patthoyts@users\.sourceforge\.net>)
[//000000004]: # (blowfish\(n\) 1\.0\.5 tcllib "Blowfish Block Cipher")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.4  
package require blowfish ?1\.0\.5?  

[__::blowfish::blowfish__ ?*\-mode \[ecb&#124;cbc\]*? ?*\-dir \[encrypt&#124;decrypt\]*? *\-key keydata* ?*\-iv vector*? ?*\-out channel*? ?*\-chunksize size*? ?*\-pad padchar*? \[ *\-in channel* &#124; ?*\-\-*? *data* \]](#1)  
[__::blowfish::Init__ *mode* *keydata* *iv*](#2)  
[__::blowfish::Encrypt__ *Key* *data*](#3)  
[__::blowfish::Decrypt__ *Key* *data*](#4)  
[__::blowfish::Reset__ *Key* *iv*](#5)  
[__::blowfish::Final__ *Key*](#6)  

[//000000001]: # (clay \- Clay Framework)
[//000000002]: # (Generated from file 'clay\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2018 Sean Woods <yoda@etoyoc\.com>)
[//000000004]: # (clay\(n\) 0\.8\.6 tcllib "Clay Framework")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

[proc __clay::dynamic\_arguments__ *ensemble* *method* *arglist* ?*args*?](#6)  
[proc __clay::dynamic\_wrongargs\_message__ *arglist*](#7)  
[proc __clay::is\_dict__ *d*](#8)  
[proc __clay::is\_null__ *value*](#9)  
[proc __clay::leaf__ ?*args*?](#10)  
[proc __clay::K__ *a* *b*](#11)  
[proc __clay::noop__ ?*args*?](#12)  
[proc __clay::cleanup__](#13)  
[proc __clay::object\_create__ *objname* ?*class* ____?](#14)  
[proc __clay::object\_rename__ *object* *newname*](#15)  
[proc __clay::object\_destroy__ ?*args*?](#16)  
[proc __clay::path__ ?*args*?](#17)  
[proc __clay::putb__ ?*map*? *text*](#18)  
[proc __clay::script\_path__](#19)  
[proc __clay::NSNormalize__ *qualname*](#20)  
[proc __clay::uuid\_generate__ ?*args*?](#21)  
[proc __clay::uuid::generate\_tcl\_machinfo__](#22)  
[proc __clay::uuid::tostring__ *uuid*](#23)  
[proc __clay::uuid::fromstring__ *uuid*](#24)  
[proc __clay::uuid::equal__ *left* *right*](#25)  
[proc __clay::uuid__ *cmd* ?*args*?](#26)  
[proc __clay::tree::sanitize__ *dict*](#27)  
[proc __clay::tree::\_sanitizeb__ *path* *varname* *dict*](#28)  
[proc __clay::tree::storage__ *rawpath*](#29)  
[proc __clay::tree::dictset__ *varname* ?*args*?](#30)  
[proc __clay::tree::dictmerge__ *varname* ?*args*?](#31)  
[proc __clay::tree::merge__ ?*args*?](#32)  
[proc __dictargs::proc__ *name* *argspec* *body*](#33)  
[proc __dictargs::method__ *name* *argspec* *body*](#34)  
[proc __clay::dialect::Push__ *class*](#35)  
[proc __clay::dialect::Peek__](#36)  
[proc __clay::dialect::Pop__](#37)  
[proc __clay::dialect::create__ *name* ?*parent* ____?](#38)  
[proc __clay::dialect::NSNormalize__ *namespace* *qualname*](#39)  
[proc __clay::dialect::DefineThunk__ *target* ?*args*?](#40)  
[proc __clay::dialect::Canonical__ *namespace* *NSpace* *class*](#41)  
[proc __clay::dialect::Define__ *namespace* *class* ?*args*?](#42)  
[proc __clay::dialect::Aliases__ *namespace* ?*args*?](#43)  
[proc __clay::dialect::SuperClass__ *namespace* ?*args*?](#44)  
[proc __clay::dynamic\_methods__ *class*](#45)  
[proc __clay::dynamic\_methods\_class__ *thisclass*](#46)  
[proc __clay::define::Array__ *name* ?*values* ____?](#47)  
[proc __clay::define::Delegate__ *name* *info*](#48)  
[proc __clay::define::constructor__ *arglist* *rawbody*](#49)  
[proc __clay::define::Class\_Method__ *name* *arglist* *body*](#50)  
[proc __clay::define::class\_method__ *name* *arglist* *body*](#51)  
[proc __clay::define::clay__ ?*args*?](#52)  
[proc __clay::define::destructor__ *rawbody*](#53)  
[proc __clay::define::Dict__ *name* ?*values* ____?](#54)  
[proc __clay::define::Option__ *name* ?*args*?](#55)  
[proc __clay::define::Method__ *name* *argstyle* *argspec* *body*](#56)  
[proc __clay::define::Option\_Class__ *name* ?*args*?](#57)  
[proc __clay::define::Variable__ *name* ?*default* ____?](#58)  
[proc __clay::ensemble\_methodbody__ *ensemble* *einfo*](#59)  
[proc __clay::define::Ensemble__ *rawmethod* ?*args*?](#60)  




[proc __clay::event::cancel__ *self* ?*task* __\*__?](#61)  
[proc __clay::event::generate__ *self* *event* ?*args*?](#62)  
[proc __clay::event::nextid__](#63)  
[proc __clay::event::Notification\_list__ *self* *event* ?*stackvar* ____?](#64)  
[proc __clay::event::notify__ *rcpt* *sender* *event* *eventinfo*](#65)  
[proc __clay::event::process__ *self* *handle* *script*](#66)  
[proc __clay::event::schedule__ *self* *handle* *interval* *script*](#67)  
[proc __clay::event::subscribe__ *self* *who* *event*](#68)  
[proc __clay::event::unsubscribe__ *self* ?*args*?](#69)  
[proc __clay::singleton__ *name* *script*](#70)  
[method __clay ancestors__](#71)  
[method __clay dump__](#72)  
[method __clay find__ *path* ?__path\.\.\.__?](#73)  
[method __clay get__ *path* ?__path\.\.\.__?](#74)  
[method __clay GET__ *path* ?__path\.\.\.__?](#75)  
[method __clay merge__ *dict* ?__dict\.\.\.__?](#76)  
[method __clay replace__ *dictionary*](#77)  
[method __clay search__ *path* ?__path\.\.\.__?](#78)  
[method __clay set__ *path* ?__path\.\.\.__? *value*](#79)  
[method __clay ancestors__](#80)  
[method __clay cache__ *path* *value*](#81)  
[method __clay cget__ *field*](#82)  
[method __clay delegate__ ?*stub*? ?*object*?](#83)  
[method __clay dump__](#84)  
[method __clay ensemble\_map__](#85)  
[method __clay eval__ *script*](#86)  
[method __clay evolve__](#87)  
[method __clay exists__ *path* ?__path\.\.\.__?](#88)  
[method __clay flush__](#89)  
[method __clay forward__ *method* *object*](#90)  
[method __clay get__ *path* ?__path\.\.\.__?](#91)  
[method __clay leaf__ *path* ?__path\.\.\.__?](#92)  
[method __clay merge__ *dict* ?__dict\.\.\.__?](#93)  
[method __clay mixin__ *class* ?__class\.\.\.__?](#94)  
[method __clay mixinmap__ ?*stub*? ?*classes*?](#95)  
[method __clay provenance__ *path* ?__path\.\.\.__?](#96)  
[method __clay replace__ *dictionary*](#97)  
[method __clay search__ *path* *valuevar* *isleafvar*](#98)  
[method __clay source__ *filename*](#99)  
[method __clay set__ *path* ?__path\.\.\.__? *value*](#100)  
[method __InitializePublic__](#101)  

# <a name='description'></a>DESCRIPTION

Clay introduces a method ensemble to both __oo::class__ and
__oo::object__ called clay\. This ensemble handles all of the high level
interactions within the framework\. Clay stores structured data\. Clan manages
method delegation\. Clay has facilities to manage the complex interactions that

  - <a name='12'></a>proc __clay::noop__ ?*args*?

    Perform a noop\. Useful in prototyping for commenting out blocks of code
    without actually having to comment them out\. It also makes a handy default
    for method delegation if a delegate has not been assigned yet\.

  - <a name='13'></a>proc __clay::cleanup__

    Process the queue of objects to be destroyed

  - <a name='14'></a>proc __clay::object\_create__ *objname* ?*class* ____?

  - <a name='15'></a>proc __clay::object\_rename__ *object* *newname*

  - <a name='16'></a>proc __clay::object\_destroy__ ?*args*?

    Mark an objects for destruction on the next cleanup

  - <a name='17'></a>proc __clay::path__ ?*args*?

  - <a name='18'></a>proc __clay::putb__ ?*map*? *text*

    Append a line of text to a variable\. Optionally apply a string mapping\.

  - <a name='19'></a>proc __clay::script\_path__

  - <a name='20'></a>proc __clay::NSNormalize__ *qualname*

  - <a name='21'></a>proc __clay::uuid\_generate__ ?*args*?

  - <a name='22'></a>proc __clay::uuid::generate\_tcl\_machinfo__

  - <a name='23'></a>proc __clay::uuid::tostring__ *uuid*

  - <a name='24'></a>proc __clay::uuid::fromstring__ *uuid*

    Convert a string representation of a uuid into its binary format\.

  - <a name='25'></a>proc __clay::uuid::equal__ *left* *right*

    Compare two uuids for equality\.

  - <a name='26'></a>proc __clay::uuid__ *cmd* ?*args*?

    uuid generate \-> string rep of a new uuid uuid equal uuid1 uuid2

  - <a name='27'></a>proc __clay::tree::sanitize__ *dict*

    Output a dictionary removing any \. entries added by
    __clay::tree::merge__

  - <a name='28'></a>proc __clay::tree::\_sanitizeb__ *path* *varname* *dict*

    Helper function for ::clay::tree::sanitize Formats the string representation
    for a dictionary element within a human readable stream of lines, and
    determines if it needs to call itself with further indentation to express a
    sub\-branch

  - <a name='29'></a>proc __clay::tree::storage__ *rawpath*

    Return the path as a storage path for clay::tree with all branch terminators
    removed\. This command will also break arguments up if they contain /\.

    Example:

    > clay::tree::storage {foo bar baz bang}
    foo bar baz bang
    > clay::tree::storage {foo bar baz bang/}
    foo bar baz bang
    > clay::tree::storage {foo bar baz bang:}
    foo bar baz bang:
    > clay::tree::storage {foo/bar/baz bang:}
    foo bar baz bang:
    > clay::tree::storage {foo/bar/baz/bang}
    foo bar baz bang

  - <a name='30'></a>proc __clay::tree::dictset__ *varname* ?*args*?

    Set an element with a recursive dictionary, marking all branches on the way
    down to the final element\. If the value does not exists in the nested
    dictionary it is added as a leaf\. If the value already exists as a branch
    the value given is merged if the value is a valid dict\. If the incoming
    value is not a valid dict, the value overrides the value stored, and the
    value is treated as a leaf from then on\.

    Example:

    > set r {}
    > ::clay::tree::dictset r option color default Green
    . {} option {. {} color {. {} default Green}}
    > ::clay::tree::dictset r option {Something not dictlike}
    . {} option {Something not dictlike}
    # Note that if the value is not a dict, and you try to force it to be
    # an error with be thrown on the merge
    > ::clay::tree::dictset r option color default Blue
    missing value to go with key

  - <a name='31'></a>proc __clay::tree::dictmerge__ *varname* ?*args*?

    A recursive form of dict merge, intended for modifying variables in place\.

    Example:

    > set mydict {sub/ {sub/ {description {a block of text}}}}
    > ::clay::tree::dictmerge mydict {sub/ {sub/ {field {another block of text}}}}]
    > clay::tree::print $mydict
    sub/ {
      sub/ {
        description {a block of text}
        field {another block of text}
      }
    }

  - <a name='32'></a>proc __clay::tree::merge__ ?*args*?

    A recursive form of dict merge

    A routine to recursively dig through dicts and merge adapted from
    http://stevehavelka\.com/tcl\-dict\-operation\-nested\-merge/

    Example:

    > set mydict {sub/ {sub/ {description {a block of text}}}}
    > set odict [clay::tree::merge $mydict {sub/ {sub/ {field {another block of text}}}}]
    > clay::tree::print $odict
    sub/ {
      sub/ {
        description {a block of text}
        field {another block of text}
      }
    }

  - <a name='33'></a>proc __dictargs::proc__ *name* *argspec* *body*

    Named Procedures as new command

  - <a name='34'></a>proc __dictargs::method__ *name* *argspec* *body*

  - <a name='35'></a>proc __clay::dialect::Push__ *class*

  - <a name='36'></a>proc __clay::dialect::Peek__

  - <a name='37'></a>proc __clay::dialect::Pop__

  - <a name='38'></a>proc __clay::dialect::create__ *name* ?*parent* ____?

    This proc will generate a namespace, a "mother of all classes", and a
    rudimentary set of policies for this dialect\.

  - <a name='39'></a>proc __clay::dialect::NSNormalize__ *namespace* *qualname*

    Support commands; not intended to be called directly\.

  - <a name='40'></a>proc __clay::dialect::DefineThunk__ *target* ?*args*?

  - <a name='41'></a>proc __clay::dialect::Canonical__ *namespace* *NSpace* *class*

  - <a name='42'></a>proc __clay::dialect::Define__ *namespace* *class* ?*args*?

    Implementation of the languages' define command

  - <a name='43'></a>proc __clay::dialect::Aliases__ *namespace* ?*args*?

  - <a name='44'></a>proc __clay::dialect::SuperClass__ *namespace* ?*args*?

  - <a name='45'></a>proc __clay::dynamic\_methods__ *class*

  - <a name='46'></a>proc __clay::dynamic\_methods\_class__ *thisclass*

  - <a name='47'></a>proc __clay::define::Array__ *name* ?*values* ____?

    New OO Keywords for clay

  - <a name='48'></a>proc __clay::define::Delegate__ *name* *info*

    An annotation that objects of this class interact with delegated methods\.
    The annotation is intended to be a dictionary, and the only reserved key is
    *description*, a human readable description\.

  - <a name='49'></a>proc __clay::define::constructor__ *arglist* *rawbody*

  - <a name='50'></a>proc __clay::define::Class\_Method__ *name* *arglist* *body*

    Specify the a method for the class object itself, instead of for objects of
    the class

  - <a name='51'></a>proc __clay::define::class\_method__ *name* *arglist* *body*

    And alias to the new Class\_Method keyword

  - <a name='52'></a>proc __clay::define::clay__ ?*args*?

  - <a name='53'></a>proc __clay::define::destructor__ *rawbody*

  - <a name='54'></a>proc __clay::define::Dict__ *name* ?*values* ____?

  - <a name='55'></a>proc __clay::define::Option__ *name* ?*args*?

    Define an option for the class

  - <a name='56'></a>proc __clay::define::Method__ *name* *argstyle* *argspec* *body*

  - <a name='57'></a>proc __clay::define::Option\_Class__ *name* ?*args*?

    Define a class of options All field / value pairs will be be inherited by an
    option that specify *name* as it class field\.

  - <a name='58'></a>proc __clay::define::Variable__ *name* ?*default* ____?

    This keyword can also be expressed:

    property variable NAME {default DEFAULT}

    Variables registered in the variable property are also initialized \(if
    missing\) when the object changes class via the *morph* method\.

  - <a name='59'></a>proc __clay::ensemble\_methodbody__ *ensemble* *einfo*

    Produce the body of an ensemble's public dispatch method ensemble is the
    name of the the ensemble\. einfo is a dictionary of methods for the ensemble,
    and each value is a script to execute on dispatch

    Example:

    ::clay::ensemble_methodbody foo {
      bar {tailcall my Foo_bar {*}$args}
      baz {tailcall my Foo_baz {*}$args}
      clock {return [clock seconds]}
      default {puts "You gave me $method"}
    }


  - <a name='60'></a>proc __clay::define::Ensemble__ *rawmethod* ?*args*?



  - <a name='61'></a>proc __clay::event::cancel__ *self* ?*task* __\*__?

    Cancel a scheduled event

  - <a name='62'></a>proc __clay::event::generate__ *self* *event* ?*args*?

    Subscribe an object to an event pattern

  - <a name='69'></a>proc __clay::event::unsubscribe__ *self* ?*args*?

    Unsubscribe an object from an event pattern

  - <a name='70'></a>proc __clay::singleton__ *name* *script*

    An object which is intended to be it's own class\.

# <a name='section3'></a>Classes

## <a name='subsection4'></a>Class  clay::class

__Methods__

  - <a name='71'></a>method __clay ancestors__

    Return this class and all ancestors in search order\.

  - <a name='72'></a>method __clay dump__

    Return a complete dump of this object's clay data, but only this object's
    clay data\.

  - <a name='73'></a>method __clay find__ *path* ?__path\.\.\.__?

    Pull a chunk of data from the clay system\. If the last element of *path*
    is a branch, returns a recursive merge of all data from this object and it's
    constituent classes of the data in that branch\. If the last element is a
    leaf, search this object for a matching leaf, or search all constituent
    classes for a matching leaf and return the first value found\. If no value is
    found, returns an empty string\. If a branch is returned the topmost \. entry
    is omitted\.

  - <a name='74'></a>method __clay get__ *path* ?__path\.\.\.__?

    Pull a chunk of data from the class's clay system\. If no value is found,
    returns an empty string\. If a branch is returned the topmost \. entry is
    omitted\.

  - <a name='75'></a>method __clay GET__ *path* ?__path\.\.\.__?

    Pull a chunk of data from the class's clay system\. If no value is found,
    returns an empty string\.

  - <a name='76'></a>method __clay merge__ *dict* ?__dict\.\.\.__?

    Recursively merge the dictionaries given into the object's local clay
    storage\.

  - <a name='77'></a>method __clay replace__ *dictionary*

    Replace the contents of the internal clay storage with the dictionary given\.

  - <a name='78'></a>method __clay search__ *path* ?__path\.\.\.__?

    Return the first matching value for the path in either this class's clay
    data or one of its ancestors

  - <a name='79'></a>method __clay set__ *path* ?__path\.\.\.__? *value*

    Merge the conents of __value__ with the object's clay storage at
    __path__\.

## <a name='subsection5'></a>Class  clay::object

clay::object This class is inherited by all classes that have options\.

__Methods__

  - <a name='80'></a>method __clay ancestors__

    Return the class this object belongs to, all classes mixed into this object,
    and all ancestors of those classes in search order\.

  - <a name='81'></a>method __clay cache__ *path* *value*

    Store VALUE in such a way that request in SEARCH for PATH will always return
    it until the cache is flushed

  - <a name='82'></a>method __clay cget__ *field*

    Pull a value from either the object's clay structure or one of its
    constituent classes that matches the field name\. The order of search us:

    1\. The as a value in local dict variable config

    2\. The as a value in local dict variable clay

    3\. As a leaf in any ancestor as a root of the clay tree

    4\. As a leaf in any ancestor as __const__ *field*

    5\. As a leaf in any ancestor as __option__ *field* __default__

  - <a name='83'></a>method __clay delegate__ ?*stub*? ?*object*?

    Introspect or control method delegation\. With no arguments, the method will
    return a key/value list of stubs and objects\. With just the *stub*
    argument, the method will return the object \(if any\) attached to the stub\.
    With a *stub* and an *object* this command will forward all calls to the
    method *stub* to the *object*\.

  - <a name='84'></a>method __clay dump__

    Return a complete dump of this object's clay data, as well as the data from
    all constituent classes recursively blended in\.

  - <a name='85'></a>method __clay ensemble\_map__

    Return a dictionary describing the method ensembles to be assembled for this
    object

  - <a name='86'></a>method __clay eval__ *script*

    Evaluated a script in the namespace of this object

  - <a name='87'></a>method __clay evolve__

    Trigger the __InitializePublic__ private method

  - <a name='88'></a>method __clay exists__ *path* ?__path\.\.\.__?

    Returns 1 if *path* exists in either the object's clay data\. Values
    greater than one indicate the element exists in one of the object's
    constituent classes\. A value of zero indicates the path could not be found\.

  - <a name='89'></a>method __clay flush__

    Wipe any caches built by the clay implementation

  - <a name='90'></a>method __clay forward__ *method* *object*

    A convenience wrapper for

    oo::objdefine [self] forward {*}$args

  - <a name='91'></a>method __clay get__ *path* ?__path\.\.\.__?

    Pull a chunk of data from the clay system\. If the last element of *path*
    is a branch \(ends in a slash /\), returns a recursive merge of all data from
    this object and it's constituent classes of the data in that branch\. If the
    last element is a leaf, search this object for a matching leaf, or search
    all constituent classes for a matching leaf and return the first value
    found\. If no value is found, returns an empty string\.

  - <a name='92'></a>method __clay leaf__ *path* ?__path\.\.\.__?

    A modified get which is tailored to pull only leaf elements

  - <a name='93'></a>method __clay merge__ *dict* ?__dict\.\.\.__?

    Recursively merge the dictionaries given into the object's local clay
    storage\.

  - <a name='94'></a>method __clay mixin__ *class* ?__class\.\.\.__?

    Perform \[oo::objdefine \[self\] mixin\] on this object, with a few additional
    rules: Prior to the call, for any class was previously mixed in, but not in
    the new result, execute the script registered to mixin/ unmap\-script \(if
    given\.\) For all new classes, that were not present prior to this call, after
    the native TclOO mixin is invoked, execute the script registered to mixin/
    map\-script \(if given\.\) Fall all classes that are now present and “mixed in”,
    execute the script registered to mixin/ react\-script \(if given\.\)

  - <a name='95'></a>method __clay mixinmap__ ?*stub*? ?*classes*?

    With no arguments returns the map of stubs and classes mixed into the
    current object\. When only stub is given, returns the classes mixed in on
    that stub\. When stub and classlist given, replace the classes currently on
    that stub with the given classes and invoke clay mixin on the new matrix of
    mixed in classes\.

  - <a name='96'></a>method __clay provenance__ *path* ?__path\.\.\.__?

    Return either __self__ if that path exists in the current object, or
    return the first class \(if any\) along the clay search path which contains
    that element\.

  - <a name='97'></a>method __clay replace__ *dictionary*

    Replace the contents of the internal clay storage with the dictionary given\.

  - <a name='98'></a>method __clay search__ *path* *valuevar* *isleafvar*

    Return true, and set valuevar to the value and isleafar to true for false if
    PATH was found in the cache\.

  - <a name='99'></a>method __clay source__ *filename*

    Source the given filename within the object's namespace

  - <a name='100'></a>method __clay set__ *path* ?__path\.\.\.__? *value*

    Merge the conents of __value__ with the object's clay storage at
    __path__\.

  - <a name='101'></a>method __InitializePublic__

    Instantiate variables\. Called on object creation and during clay mixin\.

# <a name='section4'></a>AUTHORS

Sean Woods

[//000000001]: # (debug::heartbeat \- debug narrative)
[//000000002]: # (Generated from file 'debug\_heartbeat\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright © 200?, Colin McCormack, Wub Server Utilities)
[//000000004]: # (Copyright &copy; 2012, Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>)
[//000000005]: # (debug::heartbeat\(n\) 1\.0\.1 tcllib "debug narrative")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.5  
package require debug::heartbeat ?1\.0\.1?  
package require debug ?1?  

[__[debug](debug\.md)__ __heartbeat__ ?*delta*?](#1)  

# <a name='description'></a>DESCRIPTION

# <a name='section2'></a>API

[//000000001]: # (dns \- Domain Name Service)
[//000000002]: # (Generated from file 'tcllib\_dns\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright © 2002, Pat Thoyts)
[//000000004]: # (dns\(n\) 1\.4\.1 tcllib "Domain Name Service")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.2  
package require dns ?1\.4\.1?  

[__::dns::resolve__ *query* ?*options*?](#1)  
[__::dns::configure__ ?*options*?](#2)  
[__::dns::name__ *token*](#3)  
[__::dns::address__ *token*](#4)  
[__::dns::cname__ *token*](#5)  
[__::dns::result__ *token*](#6)  

[//000000001]: # (httpd \- Tcl Web Server)
[//000000002]: # (Generated from file 'httpd\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2018 Sean Woods <yoda@etoyoc\.com>)
[//000000004]: # (httpd\(n\) 4\.3\.4 tcllib "Tcl Web Server")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

[//000000001]: # (markdown \- Markdown to HTML Converter)
[//000000002]: # (Generated from file 'markdown\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (markdown\(n\) 1\.1\.1 tcllib "Markdown to HTML Converter")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Bugs, Ideas, Feedback](#section2)

  - [Category](#category)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.5  
package require Markdown 1\.1\.1  
package require textutil ?0\.8?  

[__::Markdown::convert__ *markdown*](#1)  
[__::Markdown::register__ *langspec* *converter*](#2)  
[__::Markdown::get\_lang\_counter__](#3)  
[__::Markdown::reset\_lang\_counter__](#4)  

[__::math::geometry::h__ *length*](#8)  
[__::math::geometry::v__ *length*](#9)  
[__::math::geometry::between__ *point1* *point2* *s*](#10)  
[__::math::geometry::octant__ *point*](#11)  
[__::math::geometry::rect__ *nw* *se*](#12)  
[__::math::geometry::nwse__ *rect*](#13)  
[__::math::geometry::angle__ *line*](#14)  
[__::math::geometry::angleBetween__ *vector1* *vector2*](#15)  
[__::math::geometry::inproduct__ *vector1* *vector2*](#16)  
[__::math::geometry::areaParallellogram__ *vector1* *vector2*](#17)  
[__::math::geometry::calculateDistanceToLine__ *P* *line*](#18)  
[__::math::geometry::calculateDistanceToLineSegment__ *P* *linesegment*](#19)  
[__::math::geometry::calculateDistanceToPolyline__ *P* *polyline*](#20)  
[__::math::geometry::calculateDistanceToPolygon__ *P* *polygon*](#21)  
[__::math::geometry::findClosestPointOnLine__ *P* *line*](#22)  
[__::math::geometry::findClosestPointOnLineSegment__ *P* *linesegment*](#23)  
[__::math::geometry::findClosestPointOnPolyline__ *P* *polyline*](#24)  
[__::math::geometry::lengthOfPolyline__ *polyline*](#25)  
[__::math::geometry::movePointInDirection__ *P* *direction* *dist*](#26)  
[__::math::geometry::lineSegmentsIntersect__ *linesegment1* *linesegment2*](#27)  
[__::math::geometry::findLineSegmentIntersection__ *linesegment1* *linesegment2*](#28)  
[__::math::geometry::findLineIntersection__ *line1* *line2*](#29)  
[__::math::geometry::polylinesIntersect__ *polyline1* *polyline2*](#30)  
[__::math::geometry::polylinesBoundingIntersect__ *polyline1* *polyline2* *granularity*](#31)  
[__::math::geometry::intervalsOverlap__ *y1* *y2* *y3* *y4* *strict*](#32)  
[__::math::geometry::rectanglesOverlap__ *P1* *P2* *Q1* *Q2* *strict*](#33)  
[__::math::geometry::bbox__ *polyline*](#34)  
[__::math::geometry::pointInsidePolygon__ *P* *polyline*](#35)  
[__::math::geometry::pointInsidePolygonAlt__ *P* *polyline*](#36)  
[__::math::geometry::rectangleInsidePolygon__ *P1* *P2* *polyline*](#37)  
[__::math::geometry::areaPolygon__ *polygon*](#38)  
[__::math::geometry::translate__ *vector* *polyline*](#39)  
[__::math::geometry::rotate__ *angle* *polyline*](#40)  
[__::math::geometry::reflect__ *angle* *polyline*](#41)  
[__::math::geometry::degToRad__ *angle*](#42)  
[__::math::geometry::radToDeg__ *angle*](#43)  
[__::math::geometry::circle__ *centre* *radius*](#44)  
[__::math::geometry::circleTwoPoints__ *point1* *point2*](#45)  
[__::math::geometry::pointInsideCircle__ *point* *circle*](#46)  
[__::math::geometry::lineIntersectsCircle__ *line* *circle*](#47)  
[__::math::geometry::lineSegmentIntersectsCircle__ *segment* *circle*](#48)  
[__::math::geometry::intersectionLineWithCircle__ *line* *circle*](#49)  
[__::math::geometry::intersectionCircleWithCircle__ *circle1* *circle2*](#50)  
[__::math::geometry::tangentLinesToCircle__ *point* *circle*](#51)  

# <a name='description'></a>DESCRIPTION

The __math::geometry__ package is a collection of functions for computations
and manipulations on two\-dimensional geometrical objects, such as points, lines
and polygons\.

    Calculate the angle from the positive x\-axis to a given line \(in two
    dimensions only\)\.

      * list *line*

        Coordinates of the line

  - <a name='15'></a>__::math::geometry::angleBetween__ *vector1* *vector2*

    Calculate the angle between two vectors \(in degrees\)

      * list *vector1*

        First vector

      * list *vector2*

        Second vector

  - <a name='16'></a>__::math::geometry::inproduct__ *vector1* *vector2*

    Calculate the inner product of two vectors

      * list *vector1*

        First vector

      * list *vector2*

        Second vector

  - <a name='17'></a>__::math::geometry::areaParallellogram__ *vector1* *vector2*

    Calculate the area of the parallellogram with the two vectors as its sides

      * list *vector1*

        First vector

      * list *vector2*

        Second vector

  - <a name='18'></a>__::math::geometry::calculateDistanceToLine__ *P* *line*

    Calculate the distance of point P to the \(infinite\) line and return the
    result

      * list *P*

        List of two numbers, the coordinates of the point

      * list *line*

        List of four numbers, the coordinates of two points on the line

  - <a name='19'></a>__::math::geometry::calculateDistanceToLineSegment__ *P* *linesegment*

    Calculate the distance of point P to the \(finite\) line segment and return
    the result\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *linesegment*

        List of four numbers, the coordinates of the first and last points of
        the line segment

  - <a name='20'></a>__::math::geometry::calculateDistanceToPolyline__ *P* *polyline*

    Calculate the distance of point P to the polyline and return the result\.
    Note that a polyline needs not to be closed\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *polyline*

        List of numbers, the coordinates of the vertices of the polyline

  - <a name='21'></a>__::math::geometry::calculateDistanceToPolygon__ *P* *polygon*

    Calculate the distance of point P to the polygon and return the result\. If
    the list of coordinates is not closed \(first and last points differ\), it is
    automatically closed\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *polygon*

        List of numbers, the coordinates of the vertices of the polygon

  - <a name='22'></a>__::math::geometry::findClosestPointOnLine__ *P* *line*

    Return the point on a line which is closest to a given point\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *line*

        List of four numbers, the coordinates of two points on the line

  - <a name='23'></a>__::math::geometry::findClosestPointOnLineSegment__ *P* *linesegment*

    Return the point on a *line segment* which is closest to a given point\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *linesegment*

        List of four numbers, the first and last points on the line segment

  - <a name='24'></a>__::math::geometry::findClosestPointOnPolyline__ *P* *polyline*

    Return the point on a *polyline* which is closest to a given point\.

      * list *P*

        List of two numbers, the coordinates of the point

      * list *polyline*

        List of numbers, the vertices of the polyline

  - <a name='25'></a>__::math::geometry::lengthOfPolyline__ *polyline*

    Return the length of the *polyline* \(note: it not regarded as a polygon\)

      * list *polyline*

        List of numbers, the vertices of the polyline

  - <a name='26'></a>__::math::geometry::movePointInDirection__ *P* *direction* *dist*

    Move a point over a given distance in a given direction and return the new
    coordinates \(in two dimensions only\)\.

      * list *P*

        Coordinates of the point to be moved

      * double *direction*

        Direction \(in degrees; 0 is to the right, 90 upwards\)

      * list *dist*

        Distance over which to move the point

  - <a name='27'></a>__::math::geometry::lineSegmentsIntersect__ *linesegment1* *linesegment2*

    Check if two line segments intersect or coincide\. Returns 1 if that is the
    case, 0 otherwise \(in two dimensions only\)\. If an endpoint of one segment
    lies on the other segment \(or is very close to the segment\), they are
    considered to intersect

      * list *linesegment1*

        First line segment

      * list *linesegment2*

        Second line segment

  - <a name='28'></a>__::math::geometry::findLineSegmentIntersection__ *linesegment1* *linesegment2*

    Find the intersection point of two line segments\. Return the coordinates or
    the keywords "coincident" or "none" if the line segments coincide or have no
    points in common \(in two dimensions only\)\.

      * list *linesegment1*

        First line segment

      * list *linesegment2*

        Second line segment

  - <a name='29'></a>__::math::geometry::findLineIntersection__ *line1* *line2*

    Find the intersection point of two \(infinite\) lines\. Return the coordinates
    or the keywords "coincident" or "none" if the lines coincide or have no
    points in common \(in two dimensions only\)\.

      * list *line1*

        First line

      * list *line2*

        Second line

    See section [References](#section3) for details on the algorithm and
    math behind it\.

  - <a name='30'></a>__::math::geometry::polylinesIntersect__ *polyline1* *polyline2*

    Check if two polylines intersect or not \(in two dimensions only\)\.

      * list *polyline1*

        First polyline

      * list *polyline2*

        Second polyline

  - <a name='31'></a>__::math::geometry::polylinesBoundingIntersect__ *polyline1* *polyline2* *granularity*

    Check whether two polylines intersect, but reduce the correctness of the
    result to the given granularity\. Use this for faster, but weaker,
    intersection checking\.

    How it works:

        Second polyline

      * int *granularity*

        Number of points in each part \(<=1 means check every edge\)

  - <a name='32'></a>__::math::geometry::intervalsOverlap__ *y1* *y2* *y3* *y4* *strict*

    Check if two intervals overlap\.

      * double *y1,y2*

        Begin and end of first interval

      * double *y3,y4*

        Begin and end of second interval

      * logical *strict*

        Check for strict or non\-strict overlap

  - <a name='33'></a>__::math::geometry::rectanglesOverlap__ *P1* *P2* *Q1* *Q2* *strict*

    Check if two rectangles overlap\.

      * list *P1*

        upper\-left corner of the first rectangle

        lower\-right corner of the second rectangle

      * list *strict*

        choosing strict or non\-strict interpretation

  - <a name='34'></a>__::math::geometry::bbox__ *polyline*

    Calculate the bounding box of a polyline\. Returns a list of four
    coordinates: the upper\-left and the lower\-right corner of the box\.

      * list *polyline*

        The polyline to be examined

  - <a name='35'></a>__::math::geometry::pointInsidePolygon__ *P* *polyline*

    Determine if a point is completely inside a polygon\. If the point touches
    the polygon, then the point is not completely inside the polygon\.

      * list *P*

        Coordinates of the point

      * list *polyline*

        The polyline to be examined

  - <a name='36'></a>__::math::geometry::pointInsidePolygonAlt__ *P* *polyline*

    Determine if a point is completely inside a polygon\. If the point touches
    the polygon, then the point is not completely inside the polygon\. *Note:*
    this alternative procedure uses the so\-called winding number to determine
    this\. It handles self\-intersecting polygons in a "natural" way\.

      * list *P*

        Coordinates of the point

      * list *polyline*

        The polyline to be examined

  - <a name='37'></a>__::math::geometry::rectangleInsidePolygon__ *P1* *P2* *polyline*

    Determine if a rectangle is completely inside a polygon\. If polygon touches
    the rectangle, then the rectangle is not complete inside the polygon\.

      * list *P1*

        Upper\-left corner of the rectangle

      * list *P2*

        Lower\-right corner of the rectangle

      * list *polygon*

        The polygon in question

  - <a name='38'></a>__::math::geometry::areaPolygon__ *polygon*

    Calculate the area of a polygon\.

      * list *polygon*

        The polygon in question

  - <a name='39'></a>__::math::geometry::translate__ *vector* *polyline*

    Translate a polyline over a given vector

      * list *vector*

        Translation vector

      * list *polyline*

        The polyline to be translated

  - <a name='40'></a>__::math::geometry::rotate__ *angle* *polyline*

    Rotate a polyline over a given angle \(degrees\) around the origin

      * list *angle*

        Angle over which to rotate the polyline \(degrees\)

      * list *polyline*

        The polyline to be rotated

  - <a name='41'></a>__::math::geometry::reflect__ *angle* *polyline*

    Reflect a polyline in a line through the origin at a given angle \(degrees\)
    to the x\-axis

      * list *angle*

        Angle of the line of reflection \(degrees\)

      * list *polyline*

        The polyline to be reflected

  - <a name='42'></a>__::math::geometry::degToRad__ *angle*

    Convert from degrees to radians

      * list *angle*

        Angle in degrees

  - <a name='43'></a>__::math::geometry::radToDeg__ *angle*

    Convert from radians to degrees

      * list *angle*

        Angle in radians

  - <a name='44'></a>__::math::geometry::circle__ *centre* *radius*

    Convenience procedure to create a circle from a point and a radius\.

      * list *centre*

        Coordinates of the circle centre

      * list *radius*

        Radius of the circle

  - <a name='45'></a>__::math::geometry::circleTwoPoints__ *point1* *point2*

    Convenience procedure to create a circle from two points on its
    circumference The centre is the point between the two given points, the
    radius is half the distance between them\.

      * list *point1*

        First point

      * list *point2*

        Second point

  - <a name='46'></a>__::math::geometry::pointInsideCircle__ *point* *circle*

    Determine if the given point is inside the circle or on the circumference
    \(1\) or outside \(0\)\.

      * list *point*

        Point to be checked

      * list *circle*

        Circle that may or may not contain the point

  - <a name='47'></a>__::math::geometry::lineIntersectsCircle__ *line* *circle*

    Determine if the given line intersects the circle or touches it \(1\) or does
    not \(0\)\.

      * list *line*

        Line to be checked

      * list *circle*

        Circle that may or may not be intersected

  - <a name='48'></a>__::math::geometry::lineSegmentIntersectsCircle__ *segment* *circle*

    Determine if the given line segment intersects the circle or touches it \(1\)
    or does not \(0\)\.

      * list *segment*

        Line segment to be checked

      * list *circle*

        Circle that may or may not be intersected

  - <a name='49'></a>__::math::geometry::intersectionLineWithCircle__ *line* *circle*

    Determine the points at which the given line intersects the circle\. There
    can be zero, one or two points\. \(If the line touches the circle or is close
    to it, then one point is returned\. An arbitrary margin of 1\.0e\-10 times the
    radius is used to determine this situation\.\)

      * list *line*

        Line to be checked

      * list *circle*

        Circle that may or may not be intersected

  - <a name='50'></a>__::math::geometry::intersectionCircleWithCircle__ *circle1* *circle2*

    Determine the points at which the given two circles intersect\. There can be
    zero, one or two points\. \(If the two circles touch the circle or are very
    close, then one point is returned\. An arbitrary margin of 1\.0e\-10 times the
    mean of the radii of the two circles is used to determine this situation\.\)

      * list *circle1*

        First circle

      * list *circle2*

        Second circle

  - <a name='51'></a>__::math::geometry::tangentLinesToCircle__ *point* *circle*

    Determine the tangent lines from the given point to the circle\. There can be
    zero, one or two lines\. \(If the point is on the cirucmference or very close
    to the circle, then one line is returned\. An arbitrary margin of 1\.0e\-10
    times the radius of the circle is used to determine this situation\.\)

      * list *point*

[//000000001]: # (math::special \- Tcl Math Library)
[//000000002]: # (Generated from file 'special\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2004 Arjen Markus <arjenmarkus@users\.sourceforge\.net>)
[//000000004]: # (math::special\(n\) 0\.4 tcllib "Tcl Math Library")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl ?8\.5?  
package require math::special ?0\.4?  

[__::math::special::Beta__ *x* *y*](#1)  
[__::math::special::incBeta__ *a* *b* *x*](#2)  
[__::math::special::regIncBeta__ *a* *b* *x*](#3)  
[__::math::special::Gamma__ *x*](#4)  
[__::math::special::digamma__ *x*](#5)  
[__::math::special::erf__ *x*](#6)  
[__::math::special::erfc__ *x*](#7)  
[__::math::special::invnorm__ *p*](#8)  
[__::math::special::J0__ *x*](#9)  
[__::math::special::J1__ *x*](#10)  
[__::math::special::Jn__ *n* *x*](#11)  
[__::math::special::J1/2__ *x*](#12)  
[__::math::special::J\-1/2__ *x*](#13)  
[__::math::special::I\_n__ *x*](#14)  
[__::math::special::cn__ *u* *k*](#15)  
[__::math::special::dn__ *u* *k*](#16)  
[__::math::special::sn__ *u* *k*](#17)  
[__::math::special::elliptic\_K__ *k*](#18)  
[__::math::special::elliptic\_E__ *k*](#19)  
[__::math::special::exponential\_Ei__ *x*](#20)  
[__::math::special::exponential\_En__ *n* *x*](#21)  
[__::math::special::exponential\_li__ *x*](#22)  
[__::math::special::exponential\_Ci__ *x*](#23)  
[__::math::special::exponential\_Si__ *x*](#24)  
[__::math::special::exponential\_Chi__ *x*](#25)  
[__::math::special::exponential\_Shi__ *x*](#26)  
[__::math::special::fresnel\_C__ *x*](#27)  
[__::math::special::fresnel\_S__ *x*](#28)  
[__::math::special::sinc__ *x*](#29)  
[__::math::special::legendre__ *n*](#30)  
[__::math::special::chebyshev__ *n*](#31)  
[__::math::special::laguerre__ *alpha* *n*](#32)  
[__::math::special::hermite__ *n*](#33)  

# <a name='description'></a>DESCRIPTION

This package implements several so\-called special functions, like the Gamma
function, the Bessel functions and such\.

Each function is implemented by a procedure that bears its name \(well, in close

                 |             |             |             |
    Fresnel      | C           |  all of R   |     --      |   < 2.0e-3
    integrals    | S           |  all of R   |     --      |   < 2.0e-3
                 |             |             |             |
    general      | Beta        | (see Gamma) |     --      |   < 1.0e-9
                 | Gamma       |  x != 0,-1, |     --      |   < 1.0e-9
                 |             |  -2, ...    |             |
                 | incBeta     |             |  a, b > 0   |   < 1.0e-9
                 | regIncBeta  |             |  a, b > 0   |   < 1.0e-9
                 | digamma     |  x != 0,-1  |             |   < 1.0e-9
                 |             |  -2, ...    |             |
                 |             |             |             |
                 | sinc        |  all of R   |     --      |   exact
                 |             |             |             |
    orthogonal   | Legendre    |  all of R   | n = 0,1,... |   exact
    polynomials  | Chebyshev   |  all of R   | n = 0,1,... |   exact
                 | Laguerre    |  all of R   | n = 0,1,... |   exact
                 |             |             | alpha el. R |
                 | Hermite     |  all of R   | n = 0,1,... |   exact

*Note:* Some of the error bounds are estimated, as no "formal" bounds were
available with the implemented approximation method, others hold for the
auxiliary functions used for estimating the primary functions\.

The following well\-known functions are currently missing from the package:

  - Bessel functions of the second kind \(Y\_n, K\_n\)

  - Bessel functions of arbitrary order \(and hence the Airy functions\)

  - Chebyshev polynomials of the second kind \(U\_n\)



  - The incomplete gamma function

# <a name='section3'></a>PROCEDURES

The package defines the following public procedures:

  - <a name='1'></a>__::math::special::Beta__ *x* *y*

    Compute the Beta function for arguments "x" and "y"

      * float *x*

        First argument for the Beta function

      * float *y*

        Second argument for the Beta function

  - <a name='2'></a>__::math::special::incBeta__ *a* *b* *x*

    Compute the incomplete Beta function for argument "x" with parameters "a"
    and "b"

      * float *a*

        First parameter for the incomplete Beta function, a > 0

      * float *b*

        Second parameter for the incomplete Beta function, b > 0

      * float *x*

        Argument for the incomplete Beta function

  - <a name='3'></a>__::math::special::regIncBeta__ *a* *b* *x*

    Compute the regularized incomplete Beta function for argument "x" with
    parameters "a" and "b"

      * float *a*

        First parameter for the incomplete Beta function, a > 0

      * float *b*

        Second parameter for the incomplete Beta function, b > 0

      * float *x*

        Argument for the regularized incomplete Beta function

  - <a name='4'></a>__::math::special::Gamma__ *x*

    Compute the Gamma function for argument "x"

      * float *x*

        Argument for the Gamma function

  - <a name='5'></a>__::math::special::digamma__ *x*

    Compute the digamma function \(psi\) for argument "x"

      * float *x*

        Argument for the digamma function

  - <a name='6'></a>__::math::special::erf__ *x*

    Compute the error function for argument "x"

      * float *x*

        Argument for the error function

  - <a name='7'></a>__::math::special::erfc__ *x*

    Compute the complementary error function for argument "x"

      * float *x*

        Argument for the complementary error function

  - <a name='8'></a>__::math::special::invnorm__ *p*

    Compute the inverse of the normal distribution function for argument "p"

      * float *p*

        Argument for the inverse normal distribution function \(p must be greater
        than 0 and lower than 1\)

  - <a name='9'></a>__::math::special::J0__ *x*

    Compute the zeroth\-order Bessel function of the first kind for the argument
    "x"

      * float *x*

        Argument for the Bessel function

  - <a name='10'></a>__::math::special::J1__ *x*

    Compute the first\-order Bessel function of the first kind for the argument
    "x"

      * float *x*

        Argument for the Bessel function

  - <a name='11'></a>__::math::special::Jn__ *n* *x*

    Compute the nth\-order Bessel function of the first kind for the argument "x"

      * integer *n*

        Order of the Bessel function

      * float *x*

        Argument for the Bessel function

  - <a name='12'></a>__::math::special::J1/2__ *x*

    Compute the half\-order Bessel function of the first kind for the argument
    "x"

      * float *x*

        Argument for the Bessel function

  - <a name='13'></a>__::math::special::J\-1/2__ *x*

    Compute the minus\-half\-order Bessel function of the first kind for the
    argument "x"

      * float *x*

        Argument for the Bessel function

  - <a name='14'></a>__::math::special::I\_n__ *x*

    Compute the modified Bessel function of the first kind of order n for the
    argument "x"

      * int *x*

        Positive integer order of the function

      * float *x*

        Argument for the function

  - <a name='15'></a>__::math::special::cn__ *u* *k*

    Compute the elliptic function *cn* for the argument "u" and parameter "k"\.

      * float *u*

        Argument for the function

      * float *k*

        Parameter

  - <a name='16'></a>__::math::special::dn__ *u* *k*

    Compute the elliptic function *dn* for the argument "u" and parameter "k"\.

      * float *u*

        Argument for the function

      * float *k*

        Parameter

  - <a name='17'></a>__::math::special::sn__ *u* *k*

    Compute the elliptic function *sn* for the argument "u" and parameter "k"\.

      * float *u*

        Argument for the function

      * float *k*

        Parameter

  - <a name='18'></a>__::math::special::elliptic\_K__ *k*

    Compute the complete elliptic integral of the first kind for the argument
    "k"

      * float *k*

        Argument for the function

  - <a name='19'></a>__::math::special::elliptic\_E__ *k*

    Compute the complete elliptic integral of the second kind for the argument
    "k"

      * float *k*

        Argument for the function

  - <a name='20'></a>__::math::special::exponential\_Ei__ *x*

    Compute the exponential integral of the second kind for the argument "x"

      * float *x*

        Argument for the function \(x \!= 0\)

  - <a name='21'></a>__::math::special::exponential\_En__ *n* *x*

    Compute the exponential integral of the first kind for the argument "x" and
    order n

      * int *n*

        Order of the integral \(n >= 0\)

      * float *x*

        Argument for the function \(x >= 0\)

  - <a name='22'></a>__::math::special::exponential\_li__ *x*

    Compute the logarithmic integral for the argument "x"

      * float *x*

        Argument for the function \(x > 0\)

  - <a name='23'></a>__::math::special::exponential\_Ci__ *x*

    Compute the cosine integral for the argument "x"

      * float *x*

        Argument for the function \(x > 0\)

  - <a name='24'></a>__::math::special::exponential\_Si__ *x*

    Compute the sine integral for the argument "x"

      * float *x*

        Argument for the function \(x > 0\)

  - <a name='25'></a>__::math::special::exponential\_Chi__ *x*

    Compute the hyperbolic cosine integral for the argument "x"

      * float *x*

        Argument for the function \(x > 0\)

  - <a name='26'></a>__::math::special::exponential\_Shi__ *x*

    Compute the hyperbolic sine integral for the argument "x"

      * float *x*

        Argument for the function \(x > 0\)

  - <a name='27'></a>__::math::special::fresnel\_C__ *x*

    Compute the Fresnel cosine integral for real argument x

      * float *x*

        Argument for the function

  - <a name='28'></a>__::math::special::fresnel\_S__ *x*

    Compute the Fresnel sine integral for real argument x

      * float *x*

        Argument for the function

  - <a name='29'></a>__::math::special::sinc__ *x*

    Compute the sinc function for real argument x

      * float *x*

        Argument for the function

  - <a name='30'></a>__::math::special::legendre__ *n*

    Return the Legendre polynomial of degree n \(see [THE ORTHOGONAL
    POLYNOMIALS](#section4)\)

      * int *n*

        Degree of the polynomial

  - <a name='31'></a>__::math::special::chebyshev__ *n*

    Return the Chebyshev polynomial of degree n \(of the first kind\)

      * int *n*

        Degree of the polynomial

  - <a name='32'></a>__::math::special::laguerre__ *alpha* *n*

    Return the Laguerre polynomial of degree n with parameter alpha

      * float *alpha*

        Parameter of the Laguerre polynomial

      * int *n*

        Degree of the polynomial

  - <a name='33'></a>__::math::special::hermite__ *n*

    Return the Hermite polynomial of degree n

      * int *n*

        Degree of the polynomial

[__::math::statistics::print\-2x2__ *n11* *n21* *n12* *n22*](#31)  
[__::math::statistics::control\-xbar__ *data* ?nsamples?](#32)  
[__::math::statistics::control\-Rchart__ *data* ?nsamples?](#33)  
[__::math::statistics::test\-xbar__ *control* *data*](#34)  
[__::math::statistics::test\-Rchart__ *control* *data*](#35)  
[__::math::statistics::test\-Kruskal\-Wallis__ *confidence* *args*](#36)  
[__::math::statistics::analyse\-Kruskal\-Wallis__ *args*](#37)  
[__::math::statistics::test\-Levene__ *groups*](#38)  
[__::math::statistics::test\-Brown\-Forsythe__ *groups*](#39)  
[__::math::statistics::group\-rank__ *args*](#40)  
[__::math::statistics::test\-Wilcoxon__ *sample\_a* *sample\_b*](#41)  
[__::math::statistics::spearman\-rank__ *sample\_a* *sample\_b*](#42)  
[__::math::statistics::spearman\-rank\-extended__ *sample\_a* *sample\_b*](#43)  
[__::math::statistics::kernel\-density__ *data* opt *\-option value* \.\.\.](#44)  
[__::math::statistics::bootstrap__ *data* *sampleSize* ?numberSamples?](#45)  
[__::math::statistics::wasserstein\-distance__ *prob1* *prob2*](#46)  
[__::math::statistics::kl\-divergence__ *prob1* *prob2*](#47)  
[__::math::statistics::logistic\-model__ *xdata* *ydata*](#48)  
[__::math::statistics::logistic\-probability__ *coeffs* *x*](#49)  
[__::math::statistics::tstat__ *dof* ?alpha?](#50)  
[__::math::statistics::mv\-wls__ *wt1* *weights\_and\_values*](#51)  
[__::math::statistics::mv\-ols__ *values*](#52)  
[__::math::statistics::pdf\-normal__ *mean* *stdev* *value*](#53)  
[__::math::statistics::pdf\-lognormal__ *mean* *stdev* *value*](#54)  
[__::math::statistics::pdf\-exponential__ *mean* *value*](#55)  
[__::math::statistics::pdf\-uniform__ *xmin* *xmax* *value*](#56)  
[__::math::statistics::pdf\-triangular__ *xmin* *xmax* *value*](#57)  
[__::math::statistics::pdf\-symmetric\-triangular__ *xmin* *xmax* *value*](#58)  
[__::math::statistics::pdf\-gamma__ *alpha* *beta* *value*](#59)  
[__::math::statistics::pdf\-poisson__ *mu* *k*](#60)  
[__::math::statistics::pdf\-chisquare__ *df* *value*](#61)  
[__::math::statistics::pdf\-student\-t__ *df* *value*](#62)  
[__::math::statistics::pdf\-gamma__ *a* *b* *value*](#63)  
[__::math::statistics::pdf\-beta__ *a* *b* *value*](#64)  
[__::math::statistics::pdf\-weibull__ *scale* *shape* *value*](#65)  
[__::math::statistics::pdf\-gumbel__ *location* *scale* *value*](#66)  
[__::math::statistics::pdf\-pareto__ *scale* *shape* *value*](#67)  
[__::math::statistics::pdf\-cauchy__ *location* *scale* *value*](#68)  
[__::math::statistics::pdf\-laplace__ *location* *scale* *value*](#69)  
[__::math::statistics::pdf\-kumaraswamy__ *a* *b* *value*](#70)  
[__::math::statistics::pdf\-negative\-binomial__ *r* *p* *value*](#71)  
[__::math::statistics::cdf\-normal__ *mean* *stdev* *value*](#72)  
[__::math::statistics::cdf\-lognormal__ *mean* *stdev* *value*](#73)  
[__::math::statistics::cdf\-exponential__ *mean* *value*](#74)  
[__::math::statistics::cdf\-uniform__ *xmin* *xmax* *value*](#75)  
[__::math::statistics::cdf\-triangular__ *xmin* *xmax* *value*](#76)  
[__::math::statistics::cdf\-symmetric\-triangular__ *xmin* *xmax* *value*](#77)  
[__::math::statistics::cdf\-students\-t__ *degrees* *value*](#78)  
[__::math::statistics::cdf\-gamma__ *alpha* *beta* *value*](#79)  
[__::math::statistics::cdf\-poisson__ *mu* *k*](#80)  
[__::math::statistics::cdf\-beta__ *a* *b* *value*](#81)  
[__::math::statistics::cdf\-weibull__ *scale* *shape* *value*](#82)  
[__::math::statistics::cdf\-gumbel__ *location* *scale* *value*](#83)  
[__::math::statistics::cdf\-pareto__ *scale* *shape* *value*](#84)  
[__::math::statistics::cdf\-cauchy__ *location* *scale* *value*](#85)  
[__::math::statistics::cdf\-F__ *nf1* *nf2* *value*](#86)  
[__::math::statistics::cdf\-laplace__ *location* *scale* *value*](#87)  
[__::math::statistics::cdf\-kumaraswamy__ *a* *b* *value*](#88)  
[__::math::statistics::cdf\-negative\-binomial__ *r* *p* *value*](#89)  
[__::math::statistics::empirical\-distribution__ *values*](#90)  
[__::math::statistics::random\-normal__ *mean* *stdev* *number*](#91)  
[__::math::statistics::random\-lognormal__ *mean* *stdev* *number*](#92)  
[__::math::statistics::random\-exponential__ *mean* *number*](#93)  
[__::math::statistics::random\-uniform__ *xmin* *xmax* *number*](#94)  
[__::math::statistics::random\-triangular__ *xmin* *xmax* *number*](#95)  
[__::math::statistics::random\-symmetric\-triangular__ *xmin* *xmax* *number*](#96)  
[__::math::statistics::random\-gamma__ *alpha* *beta* *number*](#97)  
[__::math::statistics::random\-poisson__ *mu* *number*](#98)  
[__::math::statistics::random\-chisquare__ *df* *number*](#99)  
[__::math::statistics::random\-student\-t__ *df* *number*](#100)  
[__::math::statistics::random\-beta__ *a* *b* *number*](#101)  
[__::math::statistics::random\-weibull__ *scale* *shape* *number*](#102)  
[__::math::statistics::random\-gumbel__ *location* *scale* *number*](#103)  
[__::math::statistics::random\-pareto__ *scale* *shape* *number*](#104)  
[__::math::statistics::random\-cauchy__ *location* *scale* *number*](#105)  
[__::math::statistics::random\-laplace__ *location* *scale* *number*](#106)  
[__::math::statistics::random\-kumaraswamy__ *a* *b* *number*](#107)  
[__::math::statistics::random\-negative\-binomial__ *r* *p* *number*](#108)  
[__::math::statistics::histogram\-uniform__ *xmin* *xmax* *limits* *number*](#109)  
[__::math::statistics::incompleteGamma__ *x* *p* ?tol?](#110)  
[__::math::statistics::incompleteBeta__ *a* *b* *x* ?tol?](#111)  
[__::math::statistics::estimate\-pareto__ *values*](#112)  
[__::math::statistics::estimate\-exponential__ *values*](#113)  
[__::math::statistics::estimate\-laplace__ *values*](#114)  
[__::math::statistics::estimante\-negative\-binomial__ *r* *values*](#115)  
[__::math::statistics::filter__ *varname* *data* *expression*](#116)  
[__::math::statistics::map__ *varname* *data* *expression*](#117)  
[__::math::statistics::samplescount__ *varname* *list* *expression*](#118)  
[__::math::statistics::subdivide__](#119)  
[__::math::statistics::plot\-scale__ *canvas* *xmin* *xmax* *ymin* *ymax*](#120)  
[__::math::statistics::plot\-xydata__ *canvas* *xdata* *ydata* *tag*](#121)  
[__::math::statistics::plot\-xyline__ *canvas* *xdata* *ydata* *tag*](#122)  
[__::math::statistics::plot\-tdata__ *canvas* *tdata* *tag*](#123)  
[__::math::statistics::plot\-tline__ *canvas* *tdata* *tag*](#124)  
[__::math::statistics::plot\-histogram__ *canvas* *counts* *limits* *tag*](#125)  

# <a name='description'></a>DESCRIPTION

The __math::statistics__ package contains functions and procedures for basic
statistical data analysis, such as:

  - Descriptive statistical parameters \(mean, minimum, maximum, standard

    Kruskal\-Wallis statistic and the probability that that value would occur
    assuming the medians of the populations are equal\.

      * list *args*

        \- Two or more lists of data

  - <a name='38'></a>__::math::statistics::test\-Levene__ *groups*

    Compute the Levene statistic to determine if groups of data have the same
    variance \(are homoscadastic\) or not\. The data are organised in groups\. This
    version uses the mean of the data as the measure to determine the
    deviations\. The statistic is equivalent to an F statistic with degrees of
    freedom k\-1 and N\-k, k being the number of groups and N the total number of
    data\.

      * list *groups*

        \- List of groups of data

  - <a name='39'></a>__::math::statistics::test\-Brown\-Forsythe__ *groups*

    Compute the Brown\-Forsythe statistic to determine if groups of data have the
    same variance \(are homoscadastic\) or not\. Like the Levene test, but this
    version uses the median of the data\.

      * list *groups*

        \- List of groups of data

  - <a name='40'></a>__::math::statistics::group\-rank__ *args*

    Rank the groups of data with respect to the complete set\. Returns a list
    consisting of the group ID, the value and the rank \(possibly a rational
    number, in case of ties\) for each data item\.

      * list *args*

        \- Two or more lists of data

  - <a name='41'></a>__::math::statistics::test\-Wilcoxon__ *sample\_a* *sample\_b*

    Compute the Wilcoxon test statistic to determine if two samples have the
    same median or not\. \(The statistic can be regarded as standard normal, if
    the sample sizes are both larger than 10\.\) Returns the value of this
    statistic\.

      * list *sample\_a*

        \- List of data comprising the first sample

      * list *sample\_b*

        \- List of data comprising the second sample

  - <a name='42'></a>__::math::statistics::spearman\-rank__ *sample\_a* *sample\_b*

    Return the Spearman rank correlation as an alternative to the ordinary
    \(Pearson's\) correlation coefficient\. The two samples should have the same
    number of data\.

      * list *sample\_a*

        \- First list of data

      * list *sample\_b*

        \- Second list of data

  - <a name='43'></a>__::math::statistics::spearman\-rank\-extended__ *sample\_a* *sample\_b*

    Return the Spearman rank correlation as an alternative to the ordinary
    \(Pearson's\) correlation coefficient as well as additional data\. The two
    samples should have the same number of data\. The procedure returns the
    correlation coefficient, the number of data pairs used and the z\-score, an
    approximately standard normal statistic, indicating the significance of the
    correlation\.

      * list *sample\_a*

        \- First list of data

      * list *sample\_b*

        \- Second list of data

  - <a name='44'></a>__::math::statistics::kernel\-density__ *data* opt *\-option value* \.\.\.

    Return the density function based on kernel density estimation\. The
    procedure is controlled by a small set of options, each of which is given a
    reasonable default\.

    The return value consists of three lists: the centres of the bins, the
    associated probability density and a list of computational parameters \(begin

            \(default: mean \+/\- 3\*standard deviation\)

          + __\-kernel__ *function*

            Kernel to be used \(One of: gaussian, cosine, epanechnikov, uniform,
            triangular, biweight, logistic; default: gaussian\)

  - <a name='45'></a>__::math::statistics::bootstrap__ *data* *sampleSize* ?numberSamples?

    Create a subsample or subsamples from a given list of data\. The data in the
    samples are chosen from this list \- multiples may occur\. If there is only
    one subsample, the sample itself is returned \(as a list of "sampleSize"
    values\), otherwise a list of samples is returned\.

      * list *data*

        List of values to chose from

      * int *sampleSize*

        Number of values per sample

      * int *numberSamples*

        Number of samples \(default: 1\)

  - <a name='46'></a>__::math::statistics::wasserstein\-distance__ *prob1* *prob2*

    Compute the Wasserstein distance or earth mover's distance for two
    equidstantly spaced histograms or probability densities\. The histograms need
    not to be normalised to sum to one, but they must have the same number of
    entries\.

    Note: the histograms are assumed to be based on the same equidistant
    intervals\. As the bounds are not passed, the value is expressed in the
    length of the intervals\.

      * list *prob1*

        List of values for the first histogram/probability density

      * list *prob2*

        List of values for the second histogram/probability density

  - <a name='47'></a>__::math::statistics::kl\-divergence__ *prob1* *prob2*

    Compute the Kullback\-Leibler \(KL\) divergence for two equidstantly spaced
    histograms or probability densities\. The histograms need not to be
    normalised to sum to one, but they must have the same number of entries\.

    Note: the histograms are assumed to be based on the same equidistant
    intervals\. As the bounds are not passed, the value is expressed in the

        List of values for the first histogram/probability density

      * list *prob2*

        List of values for the second histogram/probability density

  - <a name='48'></a>__::math::statistics::logistic\-model__ *xdata* *ydata*

    Estimate the coefficients of the logistic model that fits the data best\. The
    data consist of independent x\-values and the outcome 0 or 1 for each of the
    x\-values\. The result can be used to estimate the probability that a certain
    x\-value gives 1\.

      * list *xdata*

        List of values for which the success \(1\) or failure \(0\) is known

      * list *ydata*

        List of successes or failures corresponding to each value in *xdata*\.

  - <a name='49'></a>__::math::statistics::logistic\-probability__ *coeffs* *x*

    Calculate the probability of success for the value *x* given the
    coefficients of the logistic model\.

      * list *coeffs*

        List of coefficients as determine by the __logistic\-model__ command

value of the t\-statistic for the specified number of degrees of freedom that is
required to demonstrate a given level of significance\.

Note: These procedures depend on the math::linearalgebra package\.

*Description of the procedures*

  - <a name='50'></a>__::math::statistics::tstat__ *dof* ?alpha?

    Returns the value of the t\-distribution t\* satisfying

        P(t*)  =  1 - alpha/2
        P(-t*) =  alpha/2

    for the number of degrees of freedom dof\.

        Number of degrees of freedom

      * float *alpha*

        Confidence level of the t\-distribution\. Defaults to 0\.05\.

  - <a name='51'></a>__::math::statistics::mv\-wls__ *wt1* *weights\_and\_values*

    Carries out a weighted least squares linear regression for the data points
    provided, with weights assigned to each point\.

    The linear model is of the form

        y = b0 + b1 * x1 + b2 * x2 ... + bN * xN + error

        A list consisting of: the weight for the first observation, the data for
        the first observation \(as a sublist\), the weight for the second
        observation \(as a sublist\) and so on\. The sublists of data are organised
        as lists of the value of the dependent variable y and the independent
        variables x1, x2 to xN\.

  - <a name='52'></a>__::math::statistics::mv\-ols__ *values*

    Carries out an ordinary least squares linear regression for the data points
    provided\.

    This procedure simply calls ::mvlinreg::wls with the weights set to 1\.0, and
    returns the same information\.

  - Histograms for the given distribution \(histogram\-\*\)

  - List of random values with the given distribution \(random\-\*\)

The following procedures have been implemented:

  - <a name='53'></a>__::math::statistics::pdf\-normal__ *mean* *stdev* *value*

    Return the probability of a given value for a normal distribution with given
    mean and standard deviation\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='54'></a>__::math::statistics::pdf\-lognormal__ *mean* *stdev* *value*

    Return the probability of a given value for a log\-normal distribution with
    given mean and standard deviation\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='55'></a>__::math::statistics::pdf\-exponential__ *mean* *value*

    Return the probability of a given value for an exponential distribution with
    given mean\.

      * float *mean*

        \- Mean value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='56'></a>__::math::statistics::pdf\-uniform__ *xmin* *xmax* *value*

    Return the probability of a given value for a uniform distribution with
    given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='57'></a>__::math::statistics::pdf\-triangular__ *xmin* *xmax* *value*

    Return the probability of a given value for a triangular distribution with
    given extremes\. If the argument min is lower than the argument max, then
    smaller values have higher probability and vice versa\. In the first case the
    probability density function is of the form *f\(x\) = 2\(1\-x\)* and the other
    case it is of the form *f\(x\) = 2x*\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='58'></a>__::math::statistics::pdf\-symmetric\-triangular__ *xmin* *xmax* *value*

    Return the probability of a given value for a symmetric triangular
    distribution with given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='59'></a>__::math::statistics::pdf\-gamma__ *alpha* *beta* *value*

    Return the probability of a given value for a Gamma distribution with given
    shape and rate parameters

      * float *alpha*

        \- Shape parameter

      * float *beta*

        \- Rate parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='60'></a>__::math::statistics::pdf\-poisson__ *mu* *k*

    Return the probability of a given number of occurrences in the same interval
    \(k\) for a Poisson distribution with given mean \(mu\)

      * float *mu*

        \- Mean number of occurrences

      * int *k*

        \- Number of occurences

  - <a name='61'></a>__::math::statistics::pdf\-chisquare__ *df* *value*

    Return the probability of a given value for a chi square distribution with
    given degrees of freedom

      * float *df*

        \- Degrees of freedom

      * float *value*

        \- Value for which the probability is required

  - <a name='62'></a>__::math::statistics::pdf\-student\-t__ *df* *value*

    Return the probability of a given value for a Student's t distribution with
    given degrees of freedom

      * float *df*

        \- Degrees of freedom

      * float *value*

        \- Value for which the probability is required

  - <a name='63'></a>__::math::statistics::pdf\-gamma__ *a* *b* *value*

    Return the probability of a given value for a Gamma distribution with given
    shape and rate parameters

      * float *a*

        \- Shape parameter

      * float *b*

        \- Rate parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='64'></a>__::math::statistics::pdf\-beta__ *a* *b* *value*

    Return the probability of a given value for a Beta distribution with given
    shape parameters

      * float *a*

        \- First shape parameter

      * float *b*

        \- Second shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='65'></a>__::math::statistics::pdf\-weibull__ *scale* *shape* *value*

    Return the probability of a given value for a Weibull distribution with
    given scale and shape parameters

      * float *location*

        \- Scale parameter

      * float *scale*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='66'></a>__::math::statistics::pdf\-gumbel__ *location* *scale* *value*

    Return the probability of a given value for a Gumbel distribution with given
    location and shape parameters

      * float *location*

        \- Location parameter

      * float *scale*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='67'></a>__::math::statistics::pdf\-pareto__ *scale* *shape* *value*

    Return the probability of a given value for a Pareto distribution with given
    scale and shape parameters

      * float *scale*

        \- Scale parameter

      * float *shape*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='68'></a>__::math::statistics::pdf\-cauchy__ *location* *scale* *value*

    Return the probability of a given value for a Cauchy distribution with given
    location and shape parameters\. Note that the Cauchy distribution has no
    finite higher\-order moments\.

      * float *location*

        \- Location parameter

      * float *scale*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='69'></a>__::math::statistics::pdf\-laplace__ *location* *scale* *value*

    Return the probability of a given value for a Laplace distribution with
    given location and shape parameters\. The Laplace distribution consists of
    two exponential functions, is peaked and has heavier tails than the normal
    distribution\.

      * float *location*

        \- Location parameter \(mean\)

      * float *scale*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='70'></a>__::math::statistics::pdf\-kumaraswamy__ *a* *b* *value*

    Return the probability of a given value for a Kumaraswamy distribution with
    given parameters a and b\. The Kumaraswamy distribution is related to the
    Beta distribution, but has a tractable cumulative distribution function\.

      * float *a*

        \- Parameter a

      * float *b*

        \- Parameter b

      * float *value*

        \- Value for which the probability is required

  - <a name='71'></a>__::math::statistics::pdf\-negative\-binomial__ *r* *p* *value*

    Return the probability of a given value for a negative binomial distribution
    with an allowed number of failures and the probability of success\.

      * int *r*

        \- Allowed number of failures \(at least 1\)

      * float *p*

        \- Probability of success

      * int *value*

        \- Number of successes for which the probability is to be returned

  - <a name='72'></a>__::math::statistics::cdf\-normal__ *mean* *stdev* *value*

    Return the cumulative probability of a given value for a normal distribution
    with given mean and standard deviation, that is the probability for values
    up to the given one\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='73'></a>__::math::statistics::cdf\-lognormal__ *mean* *stdev* *value*

    Return the cumulative probability of a given value for a log\-normal
    distribution with given mean and standard deviation, that is the probability
    for values up to the given one\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='74'></a>__::math::statistics::cdf\-exponential__ *mean* *value*

    Return the cumulative probability of a given value for an exponential
    distribution with given mean\.

      * float *mean*

        \- Mean value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='75'></a>__::math::statistics::cdf\-uniform__ *xmin* *xmax* *value*

    Return the cumulative probability of a given value for a uniform
    distribution with given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='76'></a>__::math::statistics::cdf\-triangular__ *xmin* *xmax* *value*

    Return the cumulative probability of a given value for a triangular
    distribution with given extremes\. If xmin < xmax, then lower values have a
    higher probability and vice versa, see also *pdf\-triangular*

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='77'></a>__::math::statistics::cdf\-symmetric\-triangular__ *xmin* *xmax* *value*

    Return the cumulative probability of a given value for a symmetric
    triangular distribution with given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmin*

        \- Maximum value of the distribution

      * float *value*

        \- Value for which the probability is required

  - <a name='78'></a>__::math::statistics::cdf\-students\-t__ *degrees* *value*

    Return the cumulative probability of a given value for a Student's t
    distribution with given number of degrees\.

      * int *degrees*

        \- Number of degrees of freedom

      * float *value*

        \- Value for which the probability is required

  - <a name='79'></a>__::math::statistics::cdf\-gamma__ *alpha* *beta* *value*

    Return the cumulative probability of a given value for a Gamma distribution
    with given shape and rate parameters\.

      * float *alpha*

        \- Shape parameter

      * float *beta*

        \- Rate parameter

      * float *value*

        \- Value for which the cumulative probability is required

  - <a name='80'></a>__::math::statistics::cdf\-poisson__ *mu* *k*

    Return the cumulative probability of a given number of occurrences in the
    same interval \(k\) for a Poisson distribution with given mean \(mu\)\.

      * float *mu*

        \- Mean number of occurrences

      * int *k*

        \- Number of occurences

  - <a name='81'></a>__::math::statistics::cdf\-beta__ *a* *b* *value*

    Return the cumulative probability of a given value for a Beta distribution
    with given shape parameters

      * float *a*

        \- First shape parameter

      * float *b*

        \- Second shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='82'></a>__::math::statistics::cdf\-weibull__ *scale* *shape* *value*

    Return the cumulative probability of a given value for a Weibull
    distribution with given scale and shape parameters\.

      * float *scale*

        \- Scale parameter

      * float *shape*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='83'></a>__::math::statistics::cdf\-gumbel__ *location* *scale* *value*

    Return the cumulative probability of a given value for a Gumbel distribution
    with given location and scale parameters\.

      * float *location*

        \- Location parameter

      * float *scale*

        \- Scale parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='84'></a>__::math::statistics::cdf\-pareto__ *scale* *shape* *value*

    Return the cumulative probability of a given value for a Pareto distribution
    with given scale and shape parameters

      * float *scale*

        \- Scale parameter

      * float *shape*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='85'></a>__::math::statistics::cdf\-cauchy__ *location* *scale* *value*

    Return the cumulative probability of a given value for a Cauchy distribution
    with given location and scale parameters\.

      * float *location*

        \- Location parameter

      * float *scale*

        \- Scale parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='86'></a>__::math::statistics::cdf\-F__ *nf1* *nf2* *value*

    Return the cumulative probability of a given value for an F distribution
    with nf1 and nf2 degrees of freedom\.

      * float *nf1*

        \- Degrees of freedom for the numerator

      * float *nf2*

        \- Degrees of freedom for the denominator

      * float *value*

        \- Value for which the probability is required

  - <a name='87'></a>__::math::statistics::cdf\-laplace__ *location* *scale* *value*

    Return the cumulative probability of a given value for a Laplace
    distribution with given location and shape parameters\. The Laplace
    distribution consists of two exponential functions, is peaked and has
    heavier tails than the normal distribution\.

      * float *location*

        \- Location parameter \(mean\)

      * float *scale*

        \- Shape parameter

      * float *value*

        \- Value for which the probability is required

  - <a name='88'></a>__::math::statistics::cdf\-kumaraswamy__ *a* *b* *value*

    Return the cumulative probability of a given value for a Kumaraswamy
    distribution with given parameters a and b\. The Kumaraswamy distribution is
    related to the Beta distribution, but has a tractable cumulative
    distribution function\.

      * float *a*

        \- Parameter a

      * float *b*

        \- Parameter b

      * float *value*

        \- Value for which the probability is required

  - <a name='89'></a>__::math::statistics::cdf\-negative\-binomial__ *r* *p* *value*

    Return the cumulative probability of a given value for a negative binomial
    distribution with an allowed number of failures and the probability of
    success\.

      * int *r*

        \- Allowed number of failures \(at least 1\)

      * float *p*

        \- Probability of success

      * int *value*

        \- Greatest number of successes

  - <a name='90'></a>__::math::statistics::empirical\-distribution__ *values*

    Return a list of values and their empirical probability\. The values are
    sorted in increasing order\. \(The implementation follows the description at
    the corresponding Wikipedia page\)

      * list *values*

        \- List of data to be examined

  - <a name='91'></a>__::math::statistics::random\-normal__ *mean* *stdev* *number*

    Return a list of "number" random values satisfying a normal distribution
    with given mean and standard deviation\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='92'></a>__::math::statistics::random\-lognormal__ *mean* *stdev* *number*

    Return a list of "number" random values satisfying a log\-normal distribution
    with given mean and standard deviation\.

      * float *mean*

        \- Mean value of the distribution

      * float *stdev*

        \- Standard deviation of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='93'></a>__::math::statistics::random\-exponential__ *mean* *number*

    Return a list of "number" random values satisfying an exponential
    distribution with given mean\.

      * float *mean*

        \- Mean value of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='94'></a>__::math::statistics::random\-uniform__ *xmin* *xmax* *number*

    Return a list of "number" random values satisfying a uniform distribution
    with given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmax*

        \- Maximum value of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='95'></a>__::math::statistics::random\-triangular__ *xmin* *xmax* *number*

    Return a list of "number" random values satisfying a triangular distribution
    with given extremes\. If xmin < xmax, then lower values have a higher
    probability and vice versa \(see also *pdf\-triangular*\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmax*

        \- Maximum value of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='96'></a>__::math::statistics::random\-symmetric\-triangular__ *xmin* *xmax* *number*

    Return a list of "number" random values satisfying a symmetric triangular
    distribution with given extremes\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmax*

        \- Maximum value of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='97'></a>__::math::statistics::random\-gamma__ *alpha* *beta* *number*

    Return a list of "number" random values satisfying a Gamma distribution with
    given shape and rate parameters\.

      * float *alpha*

        \- Shape parameter

      * float *beta*

        \- Rate parameter

      * int *number*

        \- Number of values to be returned

  - <a name='98'></a>__::math::statistics::random\-poisson__ *mu* *number*

    Return a list of "number" random values satisfying a Poisson distribution
    with given mean\.

      * float *mu*

        \- Mean of the distribution

      * int *number*

        \- Number of values to be returned

  - <a name='99'></a>__::math::statistics::random\-chisquare__ *df* *number*

    Return a list of "number" random values satisfying a chi square distribution
    with given degrees of freedom\.

      * float *df*

        \- Degrees of freedom

      * int *number*

        \- Number of values to be returned

  - <a name='100'></a>__::math::statistics::random\-student\-t__ *df* *number*

    Return a list of "number" random values satisfying a Student's t
    distribution with given degrees of freedom\.

      * float *df*

        \- Degrees of freedom

      * int *number*

        \- Number of values to be returned

  - <a name='101'></a>__::math::statistics::random\-beta__ *a* *b* *number*

    Return a list of "number" random values satisfying a Beta distribution with
    given shape parameters\.

      * float *a*

        \- First shape parameter

      * float *b*

        \- Second shape parameter

      * int *number*

        \- Number of values to be returned

  - <a name='102'></a>__::math::statistics::random\-weibull__ *scale* *shape* *number*

    Return a list of "number" random values satisfying a Weibull distribution
    with given scale and shape parameters\.

      * float *scale*

        \- Scale parameter

      * float *shape*

        \- Shape parameter

      * int *number*

        \- Number of values to be returned

  - <a name='103'></a>__::math::statistics::random\-gumbel__ *location* *scale* *number*

    Return a list of "number" random values satisfying a Gumbel distribution
    with given location and scale parameters\.

      * float *location*

        \- Location parameter

      * float *scale*

        \- Scale parameter

      * int *number*

        \- Number of values to be returned

  - <a name='104'></a>__::math::statistics::random\-pareto__ *scale* *shape* *number*

    Return a list of "number" random values satisfying a Pareto distribution
    with given scale and shape parameters\.

      * float *scale*

        \- Scale parameter

      * float *shape*

        \- Shape parameter

      * int *number*

        \- Number of values to be returned

  - <a name='105'></a>__::math::statistics::random\-cauchy__ *location* *scale* *number*

    Return a list of "number" random values satisfying a Cauchy distribution
    with given location and scale parameters\.

      * float *location*

        \- Location parameter

      * float *scale*

        \- Scale parameter

      * int *number*

        \- Number of values to be returned

  - <a name='106'></a>__::math::statistics::random\-laplace__ *location* *scale* *number*

    Return a list of "number" random values satisfying a Laplace distribution
    with given location and shape parameters\. The Laplace distribution consists
    of two exponential functions, is peaked and has heavier tails than the
    normal distribution\.

      * float *location*

        \- Location parameter \(mean\)

      * float *scale*

        \- Shape parameter

      * int *number*

        \- Number of values to be returned

  - <a name='107'></a>__::math::statistics::random\-kumaraswamy__ *a* *b* *number*

    Return a list of "number" random values satisying a Kumaraswamy distribution
    with given parameters a and b\. The Kumaraswamy distribution is related to
    the Beta distribution, but has a tractable cumulative distribution function\.

      * float *a*

        \- Parameter a

      * float *b*

        \- Parameter b

      * int *number*

        \- Number of values to be returned

  - <a name='108'></a>__::math::statistics::random\-negative\-binomial__ *r* *p* *number*

    Return a list of "number" random values satisying a negative binomial
    distribution\.

      * int *r*

        \- Allowed number of failures \(at least 1\)

      * float *p*

        \- Probability of success

      * int *number*

        \- Number of values to be returned

  - <a name='109'></a>__::math::statistics::histogram\-uniform__ *xmin* *xmax* *limits* *number*

    Return the expected histogram for a uniform distribution\.

      * float *xmin*

        \- Minimum value of the distribution

      * float *xmax*

        \- Maximum value of the distribution

      * list *limits*

        \- Upper limits for the buckets in the histogram

      * int *number*

        \- Total number of "observations" in the histogram

  - <a name='110'></a>__::math::statistics::incompleteGamma__ *x* *p* ?tol?

    Evaluate the incomplete Gamma integral

                  1       / x               p-1
    P(p,x) =  --------   |   dt exp(-t) * t
              Gamma(p)  / 0

      * float *x*

        \- Value of x \(limit of the integral\)

      * float *p*

        \- Value of p in the integrand

      * float *tol*

        \- Required tolerance \(default: 1\.0e\-9\)

  - <a name='111'></a>__::math::statistics::incompleteBeta__ *a* *b* *x* ?tol?

    Evaluate the incomplete Beta integral

      * float *a*

        \- First shape parameter

      * float *b*

        \- Second shape parameter

      * float *x*

        \- Value of x \(limit of the integral\)

      * float *tol*

        \- Required tolerance \(default: 1\.0e\-9\)

  - <a name='112'></a>__::math::statistics::estimate\-pareto__ *values*

    Estimate the parameters for the Pareto distribution that comes closest to
    the given values\. Returns the estimated scale and shape parameters, as well
    as the standard error for the shape parameter\.

      * list *values*

        \- List of values, assumed to be distributed according to a Pareto
        distribution

  - <a name='113'></a>__::math::statistics::estimate\-exponential__ *values*

    Estimate the parameter for the exponential distribution that comes closest
    to the given values\. Returns an estimate of the one parameter and of the
    standard error\.

      * list *values*

        \- List of values, assumed to be distributed according to an exponential
        distribution

  - <a name='114'></a>__::math::statistics::estimate\-laplace__ *values*

    Estimate the parameters for the Laplace distribution that comes closest to
    the given values\. Returns an estimate of respectively the location and scale
    parameters, based on maximum likelihood\.

      * list *values*

        \- List of values, assumed to be distributed according to an exponential
        distribution

  - <a name='115'></a>__::math::statistics::estimante\-negative\-binomial__ *r* *values*

    Estimate the probability of success for the negative binomial distribution
    that comes closest to the given values\. The allowed number of failures must
    be given\.

      * int *r*

        \- Allowed number of failures \(at least 1\)

      * int *number*

        \- List of values, assumed to be distributed according to a negative
        binomial distribution\.

TO DO: more function descriptions to be added

# <a name='section5'></a>DATA MANIPULATION

The data manipulation procedures act on lists or lists of lists:

  - <a name='116'></a>__::math::statistics::filter__ *varname* *data* *expression*

    Return a list consisting of the data for which the logical expression is
    true \(this command works analogously to the command
    __[foreach](\.\./\.\./\.\./\.\./index\.md\#foreach)__\)\.

      * string *varname*

        \- Name of the variable used in the expression

      * list *data*

        \- List of data

      * string *expression*

        \- Logical expression using the variable name

  - <a name='117'></a>__::math::statistics::map__ *varname* *data* *expression*

    Return a list consisting of the data that are transformed via the
    expression\.

      * string *varname*

        \- Name of the variable used in the expression

      * list *data*

        \- List of data

      * string *expression*

        \- Expression to be used to transform \(map\) the data

  - <a name='118'></a>__::math::statistics::samplescount__ *varname* *list* *expression*

    Return a list consisting of the *counts* of all data in the sublists of
    the "list" argument for which the expression is true\.

      * string *varname*

        \- Name of the variable used in the expression

      * list *data*

        \- List of sublists, each containing the data

      * string *expression*

        \- Logical expression to test the data \(defaults to "true"\)\.

  - <a name='119'></a>__::math::statistics::subdivide__

    Routine *PM* \- not implemented yet

# <a name='section6'></a>PLOT PROCEDURES

The following simple plotting procedures are available:

  - <a name='120'></a>__::math::statistics::plot\-scale__ *canvas* *xmin* *xmax* *ymin* *ymax*

    Set the scale for a plot in the given canvas\. All plot routines expect this
    function to be called first\. There is no automatic scaling provided\.

      * widget *canvas*

        \- Canvas widget to use

        \- Minimum y value

      * float *ymax*

        \- Maximum y value

  - <a name='121'></a>__::math::statistics::plot\-xydata__ *canvas* *xdata* *ydata* *tag*

    Create a simple XY plot in the given canvas \- the data are shown as a
    collection of dots\. The tag can be used to manipulate the appearance\.

      * widget *canvas*

        \- Canvas widget to use

      * float *xdata*

        \- Series of independent data

      * float *ydata*

        \- Series of dependent data

      * string *tag*

        \- Tag to give to the plotted data \(defaults to xyplot\)

  - <a name='122'></a>__::math::statistics::plot\-xyline__ *canvas* *xdata* *ydata* *tag*

    Create a simple XY plot in the given canvas \- the data are shown as a line
    through the data points\. The tag can be used to manipulate the appearance\.

      * widget *canvas*

        \- Canvas widget to use

      * list *xdata*

        \- Series of independent data

      * list *ydata*

        \- Series of dependent data

      * string *tag*

        \- Tag to give to the plotted data \(defaults to xyplot\)

  - <a name='123'></a>__::math::statistics::plot\-tdata__ *canvas* *tdata* *tag*

    Create a simple XY plot in the given canvas \- the data are shown as a
    collection of dots\. The horizontal coordinate is equal to the index\. The tag
    can be used to manipulate the appearance\. This type of presentation is
    suitable for autocorrelation functions for instance or for inspecting the
    time\-dependent behaviour\.

      * widget *canvas*

        \- Canvas widget to use

      * list *tdata*

        \- Series of dependent data

      * string *tag*

        \- Tag to give to the plotted data \(defaults to xyplot\)

  - <a name='124'></a>__::math::statistics::plot\-tline__ *canvas* *tdata* *tag*

    Create a simple XY plot in the given canvas \- the data are shown as a line\.
    See plot\-tdata for an explanation\.

      * widget *canvas*

        \- Canvas widget to use

      * list *tdata*

        \- Series of dependent data

      * string *tag*

        \- Tag to give to the plotted data \(defaults to xyplot\)

  - <a name='125'></a>__::math::statistics::plot\-histogram__ *canvas* *counts* *limits* *tag*

    Create a simple histogram in the given canvas

      * widget *canvas*

        \- Canvas widget to use

[//000000001]: # (practcl \- The The Proper Rational API for C to Tool Command Language Module)
[//000000002]: # (Generated from file 'practcl\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2016\-2018 Sean Woods <yoda@etoyoc\.com>)
[//000000004]: # (practcl\(n\) 0\.16\.4 tcllib "The The Proper Rational API for C to Tool Command Language Module")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - <a name='16'></a>proc __practcl::sort\_dict__ *list*

    Dictionary sort a key/value list\. Needed because pre tcl8\.6 does not have
    *lsort \-stride 2*

  - <a name='17'></a>proc __practcl::local\_os__

    Returns a dictionary describing the local operating system\. Fields return
    include:

      * download \- Filesystem path where fossil repositories and source tarballs
        are downloaded for the current user

      * EXEEXT \- The extension to give to executables\. \(i\.e\. \.exe on windows\)

      * fossil\_mirror \- A URI for a local network web server who acts as a
        fossil repository mirror

      * local\_install \- Filesystem path where packages for local consumption by
        the current user are installed

      * prefix \- The prefix as given to the Tcl core/TEA for installation to
        local\_install in \./configure

      * sandbox \- The file location where this project unpacks external projects

      * TEACUP\_PROFILE \- The ActiveState/Teacup canonical name for this platform
        \(i\.e\. win32\-ix86 macosx10\.5\-i386\-x86\_84\)

      * TEACUP\_OS \- The local operating system \(windows, macosx, openbsd, etc\)\.
        Gives the same answer as tcl\.m4, except that macosx is given as macosx
        instead of Darwin\.

      * TEA\_PLATFORM \- The platform returned by uname \-s\-uname \-r \(on Unix\), or
        "windows" on Windows

      * TEACUP\_ARCH \- The processor architecture for the local os \(i\.e\. ix86,
        x86\_64\)

      * TEACUP\_ARCH \- The processor architecture for the local os \(i\.e\. ix86,
        x86\_64\)

      * teapot \- Filesystem path where teapot package files are downloaded for
        the current user

      * userhome \- File path to store localized preferences, cache download
        files, etc for the current user

    This command uses a combination of local checks with Exec, any tclConfig\.sh
    file that is resident, autoconf data where already computed, and data
    gleaned from a file named practcl\.rc in userhome\. The location for userhome
    varies by platform and operating system:

      * Windows: ::env\(LOCALAPPDATA\)/Tcl

      * Macos: ~/Library/Application Support/Tcl

      * Other: ~/tcl

  - <a name='18'></a>proc __practcl::config\.tcl__ *path*


    A transparent call to ::practcl::read\_configuration to preserve backward
    compadibility with older copies of Practcl

  - <a name='19'></a>proc __practcl::read\_configuration__ *path*

    Detect local platform\. This command looks for data gleaned by autoconf or
    autosetup in the path specified, or perform its own logic tests if neither
    has been run\. A file named config\.site present in the location indicates
    that this project is cross compiling, and the data stored in that file is
    used for the compiler and linker\.

    This command looks for information from the following files, in the
    following order:

      * config\.tcl \- A file generated by autoconf/configure in newer editions of
        TEA, encoded as a Tcl script\.

      * config\.site \- A file containing cross compiler information, encoded as a
        SH script

      * ::env\(VisualStudioVersion\) \- On Windows, and environmental value that
        indicates MS Visual Studio is installed

    This command returns a dictionary containing all of the data cleaned from
    the sources above\. In the absence of any guidance this command returns the
    same output as ::practcl::local\_os\. In this mode, if the environmental
    variable VisualStudioVersion exists, this command will provide a template of
    fields that are appropriate for compiling on Windows under Microsoft Visual
    Studio\. The USEMSVC flag in the dictionary is a boolean flag to indicate if
    this is indeed the case\.

  - <a name='20'></a>proc __practcl::tcllib\_require__ *pkg* ?*args*?

    Try to load a package, and failing that retrieve tcllib

  - <a name='21'></a>proc __practcl::platform::tcl\_core\_options__ *os*

    Return the string to pass to \./configure to compile the Tcl core for the
    given OS\.

      * windows: \-\-with\-tzdata \-\-with\-encoding utf\-8

      * macosx: \-\-enable\-corefoundation=yes \-\-enable\-framework=no \-\-with\-tzdata
        \-\-with\-encoding utf\-8

      * other: \-\-with\-tzdata \-\-with\-encoding utf\-8

  - <a name='22'></a>proc __practcl::platform::tk\_core\_options__ *os*

  - <a name='23'></a>proc __practcl::read\_rc\_file__ *filename* ?*localdat* ____?

    Read a stylized key/value list stored in a file

  - <a name='42'></a>proc __practcl::copyDir__ *d1* *d2* ?*toplevel* __1__?

    Recursively copy the contents of *d1* to *d2*

  - <a name='43'></a>proc __practcl::buildModule__ *modpath*

  - <a name='44'></a>proc __practcl::installModule__ *modpath* *DEST*

    Install a module from MODPATH to the directory specified\. *dpath* is
    assumed to be the fully qualified path where module is to be placed\. Any
    existing files will be deleted at that path\. If the path is symlink the
    process will return with no error and no action\. If the module has contents
    in the build/ directory that are newer than the \.tcl files in the module
    source directory, and a build/build\.tcl file exists, the build/build\.tcl
    file is run\. If the source directory includes a file named index\.tcl, the
    directory is assumed to be in the tao style of modules, and the entire
    directory \(and all subdirectories\) are copied verbatim\. If no index\.tcl file
    is present, all \.tcl files are copied from the module source directory, and
    a pkgIndex\.tcl file is generated if non yet exists\. I a folder named htdocs
    exists in the source directory, that directory is copied verbatim to the
    destination\.

  - <a name='45'></a>proc __practcl::trigger__ ?*args*?

    Trigger build targets, and recompute dependencies

    Internals:

[//000000001]: # (profiler \- Tcl Profiler)
[//000000002]: # (Generated from file 'profiler\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (profiler\(n\) 0\.5 tcllib "Tcl Profiler")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Keywords](#keywords)

  - [Category](#category)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.3  
package require profiler ?0\.5?  

[__::profiler::init__](#1)  
[__::profiler::dump__ *pattern*](#2)  
[__::profiler::print__ ?*pattern*?](#3)  
[__::profiler::reset__ ?*pattern*?](#4)  
[__::profiler::suspend__ ?*pattern*?](#5)  
[__::profiler::resume__ ?*pattern*?](#6)  
[__::profiler::new\-disabled__](#7)  
[__::profiler::new\-enabled__](#8)  
[__::profiler::sortFunctions__ *key*](#9)  

# <a name='description'></a>DESCRIPTION

The __profiler__ package provides a simple Tcl source code profiler\. It is a
function\-level profiler; that is, it collects only function\-level information,
not the more detailed line\-level information\. It operates by redefining the Tcl
__[proc](\.\./\.\./\.\./\.\./index\.md\#proc)__ command\. Profiling is initiated

  - <a name='6'></a>__::profiler::resume__ ?*pattern*?

    Resume profiling for all functions matching *pattern*\. If no pattern is
    specified, profiling will be resumed for all functions\. This command should
    be invoked after suspending the profiler in the code\.

  - <a name='7'></a>__::profiler::new\-disabled__

    Change the initial profiling state for new procedures\. Invoking this command
    disables profiling for all procedures created after this command until
    __new\-enabled__ is invoked\. Activate profiling of specific procedures
    via __resume__\.

  - <a name='8'></a>__::profiler::new\-enabled__

    Change the initial profiling state for new procedures\. Invoking this command
    enables profiling for all procedures created after this command until
    __new\-disabled__ is invoked\. Prevent profiling of specific procedures
    via __suspend__\.

  - <a name='9'></a>__::profiler::sortFunctions__ *key*

    Return a list of functions sorted by a particular profiling statistic\.
    Supported values for *key* are: __calls__, __exclusiveTime__,
    __compileTime__, __nonCompileTime__, __totalRuntime__,
    __avgExclusiveTime__, and __avgRuntime__\. The return result is a
    list of lists, where each sublist consists of a function name and the value
    of *key* for that function\.

[//000000001]: # (struct::matrix \- Tcl Data Structures)
[//000000002]: # (Generated from file 'matrix\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2002\-2013,2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>)
[//000000004]: # (struct::matrix\(n\) 2\.0\.4 tcllib "Tcl Data Structures")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.2  
package require struct::matrix ?2\.0\.4?  

[__::struct::matrix__ ?*matrixName*? ?__=__&#124;__:=__&#124;__as__&#124;__deserialize__ *source*?](#1)  
[__matrixName__ *option* ?*arg arg \.\.\.*?](#2)  
[*matrixName* __=__ *sourcematrix*](#3)  
[*matrixName* __\-\->__ *destmatrix*](#4)  
[*matrixName* __add column__ ?*values*?](#5)  
[*matrixName* __add row__ ?*values*?](#6)  

# <a name='category'></a>CATEGORY

Data structures

# <a name='copyright'></a>COPYRIGHT

Copyright &copy; 2002\-2013,2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>

[//000000001]: # (struct::matrix\_v1 \- Tcl Data Structures)
[//000000002]: # (Generated from file 'matrix1\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2002,2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>)
[//000000004]: # (struct::matrix\_v1\(n\) 1\.2\.2 tcllib "Tcl Data Structures")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Category](#category)

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.2  
package require struct::matrix ?1\.2\.2?  

[__matrixName__ *option* ?*arg arg \.\.\.*?](#1)  
[*matrixName* __add column__ ?*values*?](#2)  
[*matrixName* __add row__ ?*values*?](#3)  
[*matrixName* __add columns__ *n*](#4)  
[*matrixName* __add rows__ *n*](#5)  
[*matrixName* __cells__](#6)  

# <a name='category'></a>CATEGORY

Data structures

# <a name='copyright'></a>COPYRIGHT

Copyright &copy; 2002,2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>

[//000000001]: # (tcl::chan::halfpipe \- Reflected/virtual channel support)
[//000000002]: # (Generated from file 'halfpipe\.man' by tcllib/doctools with format 'markdown')
[//000000003]: # (Copyright &copy; 2009, 2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>)
[//000000004]: # (tcl::chan::halfpipe\(n\) 1\.0\.1 tcllib "Reflected/virtual channel support")

<hr> [ <a href="../../../../toc.md">Main Table Of Contents</a> &#124; <a
href="../../../toc.md">Table Of Contents</a> &#124; <a
href="../../../../index.md">Keyword Index</a> &#124; <a
href="../../../../toc0.md">Categories</a> &#124; <a
href="../../../../toc1.md">Modules</a> &#124; <a
href="../../../../toc2.md">Applications</a> ] <hr>

  - [Copyright](#copyright)

# <a name='synopsis'></a>SYNOPSIS

package require Tcl 8\.5  
package require TclOO  
package require tcl::chan::events ?1?  
package require tcl::chan::halfpipe ?1\.0\.1?  


[__::tcl::chan::halfpipe__ ?__\-option__ *value*\.\.\.?](#1)  
[*objectCmd* __put__ *bytes*](#2)  

# <a name='description'></a>DESCRIPTION

The __tcl::chan::halfpipe__ package provides a command creating one half of

# <a name='category'></a>CATEGORY

Channels

# <a name='copyright'></a>COPYRIGHT

Copyright &copy; 2009, 2019 Andreas Kupries <andreas\_kupries@users\.sourceforge\.net>

'\"
'\" Generated from file 'blowfish\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2003, Pat Thoyts <patthoyts@users\&.sourceforge\&.net>
'\"
.TH "blowfish" n 1\&.0\&.5 tcllib "Blowfish Block Cipher"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
blowfish \- Implementation of the Blowfish block cipher
.SH SYNOPSIS
package require \fBTcl  8\&.4\fR
.sp
package require \fBblowfish  ?1\&.0\&.5?\fR
.sp
\fB::blowfish::blowfish\fR ?\fI-mode [ecb|cbc]\fR? ?\fI-dir [encrypt|decrypt]\fR? \fI-key keydata\fR ?\fI-iv vector\fR? ?\fI-out channel\fR? ?\fI-chunksize size\fR? ?\fI-pad padchar\fR? [ \fI-in channel\fR | ?\fI--\fR? \fIdata\fR ]
.sp
\fB::blowfish::Init\fR \fImode\fR \fIkeydata\fR \fIiv\fR
.sp
\fB::blowfish::Encrypt\fR \fIKey\fR \fIdata\fR
.sp

'\"
'\" Generated from file 'clay\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2018 Sean Woods <yoda@etoyoc\&.com>
'\"
.TH "clay" n 0\&.8\&.6 tcllib "Clay Framework"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

.sp
proc \fBclay::leaf\fR ?\fIargs\fR?
.sp
proc \fBclay::K\fR \fIa\fR \fIb\fR
.sp
proc \fBclay::noop\fR ?\fIargs\fR?
.sp
proc \fBclay::cleanup\fR
.sp
proc \fBclay::object_create\fR \fIobjname\fR ?\fIclass\fR \fB\fR?
.sp
proc \fBclay::object_rename\fR \fIobject\fR \fInewname\fR
.sp
proc \fBclay::object_destroy\fR ?\fIargs\fR?
.sp
proc \fBclay::path\fR ?\fIargs\fR?
.sp
proc \fBclay::putb\fR ?\fImap\fR? \fItext\fR
.sp
proc \fBclay::script_path\fR
.sp
proc \fBclay::NSNormalize\fR \fIqualname\fR

.sp
proc \fBclay::define::Variable\fR \fIname\fR ?\fIdefault\fR \fB\fR?
.sp
proc \fBclay::ensemble_methodbody\fR \fIensemble\fR \fIeinfo\fR
.sp
proc \fBclay::define::Ensemble\fR \fIrawmethod\fR ?\fIargs\fR?
.sp








proc \fBclay::event::cancel\fR \fIself\fR ?\fItask\fR \fB*\fR?
.sp
proc \fBclay::event::generate\fR \fIself\fR \fIevent\fR ?\fIargs\fR?
.sp
proc \fBclay::event::nextid\fR
.sp
proc \fBclay::event::Notification_list\fR \fIself\fR \fIevent\fR ?\fIstackvar\fR \fB\fR?
.sp
proc \fBclay::event::notify\fR \fIrcpt\fR \fIsender\fR \fIevent\fR \fIeventinfo\fR
.sp
proc \fBclay::event::process\fR \fIself\fR \fIhandle\fR \fIscript\fR
.sp
proc \fBclay::event::schedule\fR \fIself\fR \fIhandle\fR \fIinterval\fR \fIscript\fR
.sp
proc \fBclay::event::subscribe\fR \fIself\fR \fIwho\fR \fIevent\fR
.sp
proc \fBclay::event::unsubscribe\fR \fIself\fR ?\fIargs\fR?
.sp
proc \fBclay::singleton\fR \fIname\fR \fIscript\fR
.sp
method \fBclay ancestors\fR
.sp
method \fBclay dump\fR
.sp
method \fBclay find\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
.sp
method \fBclay get\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
.sp
method \fBclay GET\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
.sp
method \fBclay merge\fR \fIdict\fR ?\fBdict\&.\&.\&.\fR?
.sp
method \fBclay replace\fR \fIdictionary\fR
.sp
method \fBclay search\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
.sp
method \fBclay set\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR? \fIvalue\fR
.sp
method \fBclay ancestors\fR
.sp
method \fBclay cache\fR \fIpath\fR \fIvalue\fR
.sp
method \fBclay cget\fR \fIfield\fR
.sp
method \fBclay delegate\fR ?\fIstub\fR? ?\fIobject\fR?
.sp
method \fBclay dump\fR
.sp

method \fBclay mixin\fR \fIclass\fR ?\fBclass\&.\&.\&.\fR?
.sp
method \fBclay mixinmap\fR ?\fIstub\fR? ?\fIclasses\fR?
.sp
method \fBclay provenance\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
.sp
method \fBclay replace\fR \fIdictionary\fR
.sp
method \fBclay search\fR \fIpath\fR \fIvaluevar\fR \fIisleafvar\fR
.sp
method \fBclay source\fR \fIfilename\fR
.sp
method \fBclay set\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR? \fIvalue\fR
.sp
method \fBInitializePublic\fR
.sp

.TP
proc \fBclay::noop\fR ?\fIargs\fR?
Perform a noop\&. Useful in prototyping for commenting out blocks
of code without actually having to comment them out\&. It also makes
a handy default for method delegation if a delegate has not been
assigned yet\&.
.TP
proc \fBclay::cleanup\fR
Process the queue of objects to be destroyed
.TP
proc \fBclay::object_create\fR \fIobjname\fR ?\fIclass\fR \fB\fR?
.TP
proc \fBclay::object_rename\fR \fIobject\fR \fInewname\fR
.TP
proc \fBclay::object_destroy\fR ?\fIargs\fR?
Mark an objects for destruction on the next cleanup
.TP
proc \fBclay::path\fR ?\fIargs\fR?
.TP
proc \fBclay::putb\fR ?\fImap\fR? \fItext\fR
Append a line of text to a variable\&. Optionally apply a string mapping\&.
.TP
proc \fBclay::script_path\fR
.TP

property variable NAME {default DEFAULT}
.CE
.sp
Variables registered in the variable property are also initialized
(if missing) when the object changes class via the \fImorph\fR method\&.
.TP
proc \fBclay::ensemble_methodbody\fR \fIensemble\fR \fIeinfo\fR
Produce the body of an ensemble's public dispatch method
ensemble is the name of the the ensemble\&.
einfo is a dictionary of methods for the ensemble, and each value is a script
to execute on dispatch
.sp

Example:
.CS

 ::clay::ensemble_methodbody foo {
   bar {tailcall my Foo_bar {*}$args}
   baz {tailcall my Foo_baz {*}$args}
   clock {return [clock seconds]}
   default {puts "You gave me $method"}
 }



.CE

.TP
proc \fBclay::define::Ensemble\fR \fIrawmethod\fR ?\fIargs\fR?

.TP
proc \fBclay::event::cancel\fR \fIself\fR ?\fItask\fR \fB*\fR?
Cancel a scheduled event
.TP
proc \fBclay::event::generate\fR \fIself\fR \fIevent\fR ?\fIargs\fR?
Generate an event
Adds a subscription mechanism for objects
to see who has recieved this event and prevent

Schedule an event to occur later
.TP
proc \fBclay::event::subscribe\fR \fIself\fR \fIwho\fR \fIevent\fR
Subscribe an object to an event pattern
.TP
proc \fBclay::event::unsubscribe\fR \fIself\fR ?\fIargs\fR?
Unsubscribe an object from an event pattern
.TP
proc \fBclay::singleton\fR \fIname\fR \fIscript\fR
An object which is intended to be it's own class\&.
.PP
.SH CLASSES
.SS "CLASS  CLAY::CLASS"
.PP
\fBMethods\fR
.TP
method \fBclay ancestors\fR

This class is inherited by all classes that have options\&.
.PP
\fBMethods\fR
.TP
method \fBclay ancestors\fR
Return the class this object belongs to, all classes mixed into this object, and all ancestors of those classes in search order\&.
.TP
method \fBclay cache\fR \fIpath\fR \fIvalue\fR
Store VALUE in such a way that request in SEARCH for PATH will always return it until the cache is flushed
.TP
method \fBclay cget\fR \fIfield\fR
Pull a value from either the object's clay structure or one of its constituent classes that matches the field name\&.
The order of search us:
.sp
1\&. The as a value in local dict variable config
.sp
2\&. The as a value in local dict variable clay

.TP
method \fBclay provenance\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR?
Return either \fBself\fR if that path exists in the current object, or return the first class (if any) along the clay search path which contains that element\&.
.TP
method \fBclay replace\fR \fIdictionary\fR
Replace the contents of the internal clay storage with the dictionary given\&.
.TP
method \fBclay search\fR \fIpath\fR \fIvaluevar\fR \fIisleafvar\fR
Return true, and set valuevar to the value and isleafar to true for false if PATH was found in the cache\&.
.TP
method \fBclay source\fR \fIfilename\fR
Source the given filename within the object's namespace
.TP
method \fBclay set\fR \fIpath\fR ?\fBpath\&.\&.\&.\fR? \fIvalue\fR
Merge the conents of \fBvalue\fR with the object's clay storage at \fBpath\fR\&.
.TP
method \fBInitializePublic\fR

'\"
'\" Generated from file 'debug_heartbeat\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 200?, Colin McCormack, Wub Server Utilities
'\" Copyright (c) 2012, Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "debug::heartbeat" n 1\&.0\&.1 tcllib "debug narrative"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
debug::heartbeat \- debug narrative - heartbeat
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBdebug::heartbeat  ?1\&.0\&.1?\fR
.sp
package require \fBdebug  ?1?\fR
.sp
\fBdebug\fR \fBheartbeat\fR ?\fIdelta\fR?
.sp
.BE
.SH DESCRIPTION

'\"
'\" Generated from file 'tcllib_dns\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2002, Pat Thoyts
'\"
.TH "dns" n 1\&.4\&.1 tcllib "Domain Name Service"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
dns \- Tcl Domain Name Service Client
.SH SYNOPSIS
package require \fBTcl  8\&.2\fR
.sp
package require \fBdns  ?1\&.4\&.1?\fR
.sp
\fB::dns::resolve\fR \fIquery\fR ?\fIoptions\fR?
.sp
\fB::dns::configure\fR ?\fIoptions\fR?
.sp
\fB::dns::name\fR \fItoken\fR
.sp

'\"
'\" Generated from file 'httpd\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2018 Sean Woods <yoda@etoyoc\&.com>
'\"
.TH "httpd" n 4\&.3\&.4 tcllib "Tcl Web Server"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

'\"
'\" Generated from file 'markdown\&.man' by tcllib/doctools with format 'nroff'
'\"
.TH "markdown" n 1\&.1\&.1 tcllib "Markdown to HTML Converter"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
markdown \- Converts Markdown text to HTML
.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBMarkdown  1\&.1\&.1\fR
.sp
package require \fBtextutil  ?0\&.8?\fR
.sp
\fB::Markdown::convert\fR \fImarkdown\fR
.sp
\fB::Markdown::register\fR \fIlangspec\fR \fIconverter\fR
.sp

.sp
\fB::math::geometry::rect\fR \fInw\fR \fIse\fR
.sp
\fB::math::geometry::nwse\fR \fIrect\fR
.sp
\fB::math::geometry::angle\fR \fIline\fR
.sp
\fB::math::geometry::angleBetween\fR \fIvector1\fR \fIvector2\fR
.sp
\fB::math::geometry::inproduct\fR \fIvector1\fR \fIvector2\fR
.sp
\fB::math::geometry::areaParallellogram\fR \fIvector1\fR \fIvector2\fR
.sp
\fB::math::geometry::calculateDistanceToLine\fR \fIP\fR \fIline\fR
.sp
\fB::math::geometry::calculateDistanceToLineSegment\fR \fIP\fR \fIlinesegment\fR
.sp
\fB::math::geometry::calculateDistanceToPolyline\fR \fIP\fR \fIpolyline\fR
.sp
\fB::math::geometry::calculateDistanceToPolygon\fR \fIP\fR \fIpolygon\fR

Calculate the angle from the positive x-axis to a given line
(in two dimensions only)\&.
.RS
.TP
list \fIline\fR
Coordinates of the line
.RE
.TP
\fB::math::geometry::angleBetween\fR \fIvector1\fR \fIvector2\fR
Calculate the angle between two vectors (in degrees)
.RS
.TP
list \fIvector1\fR
First vector
.TP
list \fIvector2\fR
Second vector
.RE
.TP
\fB::math::geometry::inproduct\fR \fIvector1\fR \fIvector2\fR
Calculate the inner product of two vectors
.RS
.TP
list \fIvector1\fR
First vector
.TP
list \fIvector2\fR
Second vector
.RE
.TP
\fB::math::geometry::areaParallellogram\fR \fIvector1\fR \fIvector2\fR
Calculate the area of the parallellogram with the two vectors as its sides
.RS
.TP
list \fIvector1\fR
First vector
.TP
list \fIvector2\fR
Second vector
.RE
.sp
.TP
\fB::math::geometry::calculateDistanceToLine\fR \fIP\fR \fIline\fR
Calculate the distance of point P to the (infinite) line and return the
result
.RS
.TP

Translate a polyline over a given vector
.RS
.TP
list \fIvector\fR
Translation vector
.TP
list \fIpolyline\fR
The polyline to be translated
.RE
.sp
.TP
\fB::math::geometry::rotate\fR \fIangle\fR \fIpolyline\fR
Rotate a polyline over a given angle (degrees) around the origin
.RS
.TP
list \fIangle\fR
Angle over which to rotate the polyline (degrees)
.TP
list \fIpolyline\fR
The polyline to be rotated
.RE
.sp
.TP
\fB::math::geometry::reflect\fR \fIangle\fR \fIpolyline\fR
Reflect a polyline in a line through the origin at a given angle (degrees) to the x-axis
.RS
.TP

'\"
'\" Generated from file 'special\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>
'\"
.TH "math::special" n 0\&.4 tcllib "Tcl Math Library"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

.de MT
.QW ""
..
.BS
.SH NAME
math::special \- Special mathematical functions
.SH SYNOPSIS
package require \fBTcl  ?8\&.5?\fR
.sp
package require \fBmath::special  ?0\&.4?\fR
.sp
\fB::math::special::Beta\fR \fIx\fR \fIy\fR
.sp
\fB::math::special::incBeta\fR \fIa\fR \fIb\fR \fIx\fR
.sp
\fB::math::special::regIncBeta\fR \fIa\fR \fIb\fR \fIx\fR
.sp
\fB::math::special::Gamma\fR \fIx\fR
.sp
\fB::math::special::digamma\fR \fIx\fR
.sp
\fB::math::special::erf\fR \fIx\fR
.sp
\fB::math::special::erfc\fR \fIx\fR
.sp
\fB::math::special::invnorm\fR \fIp\fR
.sp

             |             |             |             |
Fresnel      | C           |  all of R   |     --      |   < 2\&.0e-3
integrals    | S           |  all of R   |     --      |   < 2\&.0e-3
             |             |             |             |
general      | Beta        | (see Gamma) |     --      |   < 1\&.0e-9
             | Gamma       |  x != 0,-1, |     --      |   < 1\&.0e-9
             |             |  -2, \&.\&.\&.    |             |
             | incBeta     |             |  a, b > 0   |   < 1\&.0e-9
             | regIncBeta  |             |  a, b > 0   |   < 1\&.0e-9
             | digamma     |  x != 0,-1  |             |   < 1\&.0e-9
             |             |  -2, \&.\&.\&.    |             |
             |             |             |             |
             | sinc        |  all of R   |     --      |   exact
             |             |             |             |
orthogonal   | Legendre    |  all of R   | n = 0,1,\&.\&.\&. |   exact
polynomials  | Chebyshev   |  all of R   | n = 0,1,\&.\&.\&. |   exact
             | Laguerre    |  all of R   | n = 0,1,\&.\&.\&. |   exact
             |             |             | alpha el\&. R |
             | Hermite     |  all of R   | n = 0,1,\&.\&.\&. |   exact

.IP \(bu
Bessel functions of the second kind (Y_n, K_n)
.IP \(bu
Bessel functions of arbitrary order (and hence the Airy functions)
.IP \(bu
Chebyshev polynomials of the second kind (U_n)
.IP \(bu


The incomplete gamma function
.PP
.SH PROCEDURES
The package defines the following public procedures:
.TP
\fB::math::special::Beta\fR \fIx\fR \fIy\fR
Compute the Beta function for arguments "x" and "y"
.RS
.TP
float \fIx\fR
First argument for the Beta function
.TP
float \fIy\fR
Second argument for the Beta function
.RE
.sp
.TP
\fB::math::special::incBeta\fR \fIa\fR \fIb\fR \fIx\fR
Compute the incomplete Beta function for argument "x" with parameters "a" and "b"
.RS
.TP
float \fIa\fR
First parameter for the incomplete Beta function, a > 0
.TP
float \fIb\fR
Second parameter for the incomplete Beta function, b > 0
.TP
float \fIx\fR
Argument for the incomplete Beta function
.RE
.sp
.TP
\fB::math::special::regIncBeta\fR \fIa\fR \fIb\fR \fIx\fR
Compute the regularized incomplete Beta function for argument "x" with parameters "a" and "b"
.RS
.TP
float \fIa\fR
First parameter for the incomplete Beta function, a > 0
.TP
float \fIb\fR
Second parameter for the incomplete Beta function, b > 0
.TP
float \fIx\fR
Argument for the regularized incomplete Beta function
.RE
.sp
.TP
\fB::math::special::Gamma\fR \fIx\fR
Compute the Gamma function for argument "x"
.RS
.TP
float \fIx\fR
Argument for the Gamma function
.RE
.sp
.TP
\fB::math::special::digamma\fR \fIx\fR
Compute the digamma function (psi) for argument "x"
.RS
.TP
float \fIx\fR
Argument for the digamma function
.RE
.sp
.TP
\fB::math::special::erf\fR \fIx\fR
Compute the error function for argument "x"
.RS
.TP
float \fIx\fR

.sp
\fB::math::statistics::test-Rchart\fR \fIcontrol\fR \fIdata\fR
.sp
\fB::math::statistics::test-Kruskal-Wallis\fR \fIconfidence\fR \fIargs\fR
.sp
\fB::math::statistics::analyse-Kruskal-Wallis\fR \fIargs\fR
.sp
\fB::math::statistics::test-Levene\fR \fIgroups\fR
.sp
\fB::math::statistics::test-Brown-Forsythe\fR \fIgroups\fR
.sp
\fB::math::statistics::group-rank\fR \fIargs\fR
.sp
\fB::math::statistics::test-Wilcoxon\fR \fIsample_a\fR \fIsample_b\fR
.sp
\fB::math::statistics::spearman-rank\fR \fIsample_a\fR \fIsample_b\fR
.sp
\fB::math::statistics::spearman-rank-extended\fR \fIsample_a\fR \fIsample_b\fR

.sp
\fB::math::statistics::pdf-gumbel\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::pdf-pareto\fR \fIscale\fR \fIshape\fR \fIvalue\fR
.sp
\fB::math::statistics::pdf-cauchy\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::pdf-laplace\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::pdf-kumaraswamy\fR \fIa\fR \fIb\fR \fIvalue\fR
.sp
\fB::math::statistics::pdf-negative-binomial\fR \fIr\fR \fIp\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-normal\fR \fImean\fR \fIstdev\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-lognormal\fR \fImean\fR \fIstdev\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-exponential\fR \fImean\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-uniform\fR \fIxmin\fR \fIxmax\fR \fIvalue\fR

\fB::math::statistics::cdf-gumbel\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-pareto\fR \fIscale\fR \fIshape\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-cauchy\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-F\fR \fInf1\fR \fInf2\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-laplace\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-kumaraswamy\fR \fIa\fR \fIb\fR \fIvalue\fR
.sp
\fB::math::statistics::cdf-negative-binomial\fR \fIr\fR \fIp\fR \fIvalue\fR
.sp
\fB::math::statistics::empirical-distribution\fR \fIvalues\fR
.sp
\fB::math::statistics::random-normal\fR \fImean\fR \fIstdev\fR \fInumber\fR
.sp
\fB::math::statistics::random-lognormal\fR \fImean\fR \fIstdev\fR \fInumber\fR
.sp

\fB::math::statistics::random-weibull\fR \fIscale\fR \fIshape\fR \fInumber\fR
.sp
\fB::math::statistics::random-gumbel\fR \fIlocation\fR \fIscale\fR \fInumber\fR
.sp
\fB::math::statistics::random-pareto\fR \fIscale\fR \fIshape\fR \fInumber\fR
.sp
\fB::math::statistics::random-cauchy\fR \fIlocation\fR \fIscale\fR \fInumber\fR
.sp
\fB::math::statistics::random-laplace\fR \fIlocation\fR \fIscale\fR \fInumber\fR
.sp
\fB::math::statistics::random-kumaraswamy\fR \fIa\fR \fIb\fR \fInumber\fR
.sp
\fB::math::statistics::random-negative-binomial\fR \fIr\fR \fIp\fR \fInumber\fR
.sp
\fB::math::statistics::histogram-uniform\fR \fIxmin\fR \fIxmax\fR \fIlimits\fR \fInumber\fR
.sp
\fB::math::statistics::incompleteGamma\fR \fIx\fR \fIp\fR ?tol?
.sp
\fB::math::statistics::incompleteBeta\fR \fIa\fR \fIb\fR \fIx\fR ?tol?
.sp
\fB::math::statistics::estimate-pareto\fR \fIvalues\fR
.sp
\fB::math::statistics::estimate-exponential\fR \fIvalues\fR
.sp
\fB::math::statistics::estimate-laplace\fR \fIvalues\fR
.sp
\fB::math::statistics::estimante-negative-binomial\fR \fIr\fR \fIvalues\fR
.sp
\fB::math::statistics::filter\fR \fIvarname\fR \fIdata\fR \fIexpression\fR
.sp
\fB::math::statistics::map\fR \fIvarname\fR \fIdata\fR \fIexpression\fR
.sp
\fB::math::statistics::samplescount\fR \fIvarname\fR \fIlist\fR \fIexpression\fR
.sp
\fB::math::statistics::subdivide\fR

equal\&.
.RS
.TP
list \fIargs\fR
- Two or more lists of data
.RE
.sp
.TP
\fB::math::statistics::test-Levene\fR \fIgroups\fR
Compute the Levene statistic to determine if groups of data have the
same variance (are homoscadastic) or not\&. The data are organised
in groups\&. This version uses the mean of the data as the measure
to determine the deviations\&. The statistic is equivalent to an
F statistic with degrees of freedom k-1 and N-k, k being the
number of groups and N the total number of data\&.
.RS
.TP
list \fIgroups\fR
- List of groups of data
.RE
.sp
.TP
\fB::math::statistics::test-Brown-Forsythe\fR \fIgroups\fR
Compute the Brown-Forsythe statistic to determine if groups of data have the
same variance (are homoscadastic) or not\&. Like the Levene test, but this
version uses the median of the data\&.
.RS
.TP
list \fIgroups\fR
- List of groups of data
.RE
.sp
.TP
\fB::math::statistics::group-rank\fR \fIargs\fR
Rank the groups of data with respect to the complete set\&.
Returns a list consisting of the group ID, the value and the rank
(possibly a rational number, in case of ties) for each data item\&.
.RS
.TP
list \fIargs\fR
- Two or more lists of data
.RE
.sp
.TP
\fB::math::statistics::test-Wilcoxon\fR \fIsample_a\fR \fIsample_b\fR
Compute the Wilcoxon test statistic to determine if two samples have the
same median or not\&. (The statistic can be regarded as standard normal, if the
sample sizes are both larger than 10\&.) Returns the value of this statistic\&.
.RS
.TP
list \fIsample_a\fR
- List of data comprising the first sample
.TP
list \fIsample_b\fR
- List of data comprising the second sample

float \fIscale\fR
- Shape parameter
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::pdf-laplace\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
Return the probability of a given value for a Laplace
distribution with given location and shape parameters\&. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution\&.
.RS
.TP
float \fIlocation\fR
- Location parameter (mean)
.TP
float \fIscale\fR
- Shape parameter
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::pdf-kumaraswamy\fR \fIa\fR \fIb\fR \fIvalue\fR
Return the probability of a given value for a Kumaraswamy
distribution with given parameters a and b\&. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function\&.
.RS
.TP
float \fIa\fR
- Parameter a
.TP
float \fIb\fR
- Parameter b
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::pdf-negative-binomial\fR \fIr\fR \fIp\fR \fIvalue\fR
Return the probability of a given value for a negative binomial
distribution with an allowed number of failures and the probability of success\&.
.RS
.TP
int \fIr\fR
- Allowed number of failures (at least 1)
.TP
float \fIp\fR
- Probability of success
.TP
int \fIvalue\fR
- Number of successes for which the probability is to be returned
.RE
.sp
.TP
\fB::math::statistics::cdf-normal\fR \fImean\fR \fIstdev\fR \fIvalue\fR
Return the cumulative probability of a given value for a normal
distribution with given mean and standard deviation, that is the
probability for values up to the given one\&.
.RS
.TP

.TP
float \fInf2\fR
- Degrees of freedom for the denominator
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::cdf-laplace\fR \fIlocation\fR \fIscale\fR \fIvalue\fR
Return the cumulative probability of a given value for a Laplace
distribution with given location and shape parameters\&. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution\&.
.RS
.TP
float \fIlocation\fR
- Location parameter (mean)
.TP
float \fIscale\fR
- Shape parameter
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::cdf-kumaraswamy\fR \fIa\fR \fIb\fR \fIvalue\fR
Return the cumulative probability of a given value for a Kumaraswamy
distribution with given parameters a and b\&. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function\&.
.RS
.TP
float \fIa\fR
- Parameter a
.TP
float \fIb\fR
- Parameter b
.TP
float \fIvalue\fR
- Value for which the probability is required
.RE
.sp
.TP
\fB::math::statistics::cdf-negative-binomial\fR \fIr\fR \fIp\fR \fIvalue\fR
Return the cumulative probability of a given value for a negative binomial
distribution with an allowed number of failures and the probability of success\&.
.RS
.TP
int \fIr\fR
- Allowed number of failures (at least 1)
.TP
float \fIp\fR
- Probability of success
.TP
int \fIvalue\fR
- Greatest number of successes
.RE
.sp
.TP
\fB::math::statistics::empirical-distribution\fR \fIvalues\fR
Return a list of values and their empirical probability\&. The values are sorted in increasing order\&.
(The implementation follows the description at the corresponding Wikipedia page)
.RS
.TP

float \fIscale\fR
- Scale parameter
.TP
int \fInumber\fR
- Number of values to be returned
.RE
.sp
.TP
\fB::math::statistics::random-laplace\fR \fIlocation\fR \fIscale\fR \fInumber\fR
Return a list of "number" random values satisfying a Laplace
distribution with given location and shape parameters\&. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution\&.
.RS
.TP
float \fIlocation\fR
- Location parameter (mean)
.TP
float \fIscale\fR
- Shape parameter
.TP
int \fInumber\fR
- Number of values to be returned
.RE
.sp
.TP
\fB::math::statistics::random-kumaraswamy\fR \fIa\fR \fIb\fR \fInumber\fR
Return a list of "number" random values satisying a Kumaraswamy
distribution with given parameters a and b\&. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function\&.
.RS
.TP
float \fIa\fR
- Parameter a
.TP
float \fIb\fR
- Parameter b
.TP
int \fInumber\fR
- Number of values to be returned
.RE
.sp
.TP
\fB::math::statistics::random-negative-binomial\fR \fIr\fR \fIp\fR \fInumber\fR
Return a list of "number" random values satisying a negative binomial distribution\&.
.RS
.TP
int \fIr\fR
- Allowed number of failures (at least 1)
.TP
float \fIp\fR
- Probability of success
.TP
int \fInumber\fR
- Number of values to be returned
.RE
.sp
.TP
\fB::math::statistics::histogram-uniform\fR \fIxmin\fR \fIxmax\fR \fIlimits\fR \fInumber\fR
Return the expected histogram for a uniform distribution\&.
.RS
.TP
float \fIxmin\fR
- Minimum value of the distribution

Estimate the parameter for the exponential distribution that comes closest to the given values\&.
Returns an estimate of the one parameter and of the standard error\&.
.RS
.TP
list \fIvalues\fR
- List of values, assumed to be distributed according to an exponential distribution
.RE
.sp
.TP
\fB::math::statistics::estimate-laplace\fR \fIvalues\fR
Estimate the parameters for the Laplace distribution that comes closest to the given values\&.
Returns an estimate of respectively the location and scale parameters, based on maximum likelihood\&.
.RS
.TP
list \fIvalues\fR
- List of values, assumed to be distributed according to an exponential distribution
.RE
.sp
.TP
\fB::math::statistics::estimante-negative-binomial\fR \fIr\fR \fIvalues\fR
Estimate the probability of success for the negative binomial distribution that comes closest to the given values\&.
The allowed number of failures must be given\&.
.RS
.TP
int \fIr\fR
- Allowed number of failures (at least 1)
.TP
int \fInumber\fR
- List of values, assumed to be distributed according to a negative binomial distribution\&.
.RE
.sp
.PP
TO DO: more function descriptions to be added
.SH "DATA MANIPULATION"
The data manipulation procedures act on lists or lists of lists:
.TP
\fB::math::statistics::filter\fR \fIvarname\fR \fIdata\fR \fIexpression\fR

'\"
'\" Generated from file 'practcl\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2016-2018 Sean Woods <yoda@etoyoc\&.com>
'\"
.TH "practcl" n 0\&.16\&.4 tcllib "The The Proper Rational API for C to Tool Command Language Module"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

on older interpreters this invokes zip via exec
.TP
proc \fBpractcl::sort_dict\fR \fIlist\fR
Dictionary sort a key/value list\&. Needed because pre tcl8\&.6
does not have \fIlsort -stride 2\fR
.TP
proc \fBpractcl::local_os\fR
Returns a dictionary describing the local operating system\&.
Fields return include:
.RS
.IP \(bu
download - Filesystem path where fossil repositories and source tarballs are downloaded for the current user
.IP \(bu
EXEEXT - The extension to give to executables\&. (i\&.e\&. \&.exe on windows)
.IP \(bu
fossil_mirror - A URI for a local network web server who acts as a fossil repository mirror
.IP \(bu
local_install - Filesystem path where packages for local consumption by the current user are installed
.IP \(bu
prefix - The prefix as given to the Tcl core/TEA for installation to local_install in \&./configure
.IP \(bu
sandbox - The file location where this project unpacks external projects
.IP \(bu
TEACUP_PROFILE - The ActiveState/Teacup canonical name for this platform (i\&.e\&. win32-ix86 macosx10\&.5-i386-x86_84)
.IP \(bu
TEACUP_OS - The local operating system (windows, macosx, openbsd, etc)\&. Gives the same answer as tcl\&.m4, except that macosx is given as macosx instead of Darwin\&.
.IP \(bu
TEA_PLATFORM - The platform returned by uname -s-uname -r (on Unix), or "windows" on Windows
.IP \(bu
TEACUP_ARCH - The processor architecture for the local os (i\&.e\&. ix86, x86_64)
.IP \(bu
TEACUP_ARCH - The processor architecture for the local os (i\&.e\&. ix86, x86_64)
.IP \(bu
teapot - Filesystem path where teapot package files are downloaded for the current user
.IP \(bu
userhome - File path to store localized preferences, cache download files, etc for the current user
.RE
.IP
This command uses a combination of local checks with Exec, any tclConfig\&.sh file that is
resident, autoconf data where already computed, and data gleaned from a file named
practcl\&.rc in userhome\&. The location for userhome varies by platform and operating system:
.RS
.IP \(bu
Windows: ::env(LOCALAPPDATA)/Tcl
.IP \(bu
Macos: ~/Library/Application Support/Tcl
.IP \(bu
Other: ~/tcl
.RE
.TP
proc \fBpractcl::config\&.tcl\fR \fIpath\fR

A transparent call to ::practcl::read_configuration to preserve backward compadibility
with older copies of Practcl
.TP
proc \fBpractcl::read_configuration\fR \fIpath\fR
Detect local platform\&. This command looks for data gleaned by autoconf or autosetup
in the path specified, or perform its own logic tests if neither has been run\&.
A file named config\&.site present in the location indicates that this project is
cross compiling, and the data stored in that file is used for the compiler and linker\&.
.sp
This command looks for information from the following files, in the following order:
.RS
.IP \(bu
config\&.tcl - A file generated by autoconf/configure in newer editions of TEA, encoded as a Tcl script\&.
.IP \(bu
config\&.site - A file containing cross compiler information, encoded as a SH script
.IP \(bu
::env(VisualStudioVersion) - On Windows, and environmental value that indicates MS Visual Studio is installed
.RE
.sp
This command returns a dictionary containing all of the data cleaned from the sources above\&.
In the absence of any guidance this command returns the same output as ::practcl::local_os\&.
In this mode, if the environmental variable VisualStudioVersion exists, this command
will provide a template of fields that are appropriate for compiling on Windows under
Microsoft Visual Studio\&. The USEMSVC flag in the dictionary is a boolean flag to indicate
if this is indeed the case\&.
.TP
proc \fBpractcl::tcllib_require\fR \fIpkg\fR ?\fIargs\fR?
Try to load  a package, and failing that
retrieve tcllib
.TP
proc \fBpractcl::platform::tcl_core_options\fR \fIos\fR
Return the string to pass to \&./configure to compile the Tcl core for the given OS\&.
.RS
.IP \(bu
windows: --with-tzdata --with-encoding utf-8
.IP \(bu
macosx: --enable-corefoundation=yes  --enable-framework=no --with-tzdata --with-encoding utf-8
.IP \(bu
other: --with-tzdata --with-encoding utf-8
.RE
.TP
proc \fBpractcl::platform::tk_core_options\fR \fIos\fR
.TP
proc \fBpractcl::read_rc_file\fR \fIfilename\fR ?\fIlocaldat\fR \fB\fR?
Read a stylized key/value list stored in a file
.TP
proc \fBpractcl::read_sh_subst\fR \fIline\fR \fIinfo\fR

.TP
proc \fBpractcl::copyDir\fR \fId1\fR \fId2\fR ?\fItoplevel\fR \fB1\fR?
Recursively copy the contents of \fId1\fR to \fId2\fR
.TP
proc \fBpractcl::buildModule\fR \fImodpath\fR
.TP
proc \fBpractcl::installModule\fR \fImodpath\fR \fIDEST\fR
Install a module from MODPATH to the directory specified\&.
\fIdpath\fR is assumed to be the fully qualified path where module is to be placed\&.
Any existing files will be deleted at that path\&.
If the path is symlink the process will return with no error and no action\&.
If the module has contents in the build/ directory that are newer than the
\&.tcl files in the module source directory, and a build/build\&.tcl file exists,
the build/build\&.tcl file is run\&.
If the source directory includes a file named index\&.tcl, the directory is assumed
to be in the tao style of modules, and the entire directory (and all subdirectories)
are copied verbatim\&.
If no index\&.tcl file is present, all \&.tcl files are copied from the module source
directory, and a pkgIndex\&.tcl file is generated if non yet exists\&.
I a folder named htdocs exists in the source directory, that directory is copied
verbatim to the destination\&.
.TP
proc \fBpractcl::trigger\fR ?\fIargs\fR?
Trigger build targets, and recompute dependencies
.sp
Internals:
.CS

'\"
'\" Generated from file 'profiler\&.man' by tcllib/doctools with format 'nroff'
'\"
.TH "profiler" n 0\&.5 tcllib "Tcl Profiler"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
profiler \- Tcl source code profiler
.SH SYNOPSIS
package require \fBTcl  8\&.3\fR
.sp
package require \fBprofiler  ?0\&.5?\fR
.sp
\fB::profiler::init\fR
.sp
\fB::profiler::dump\fR \fIpattern\fR
.sp
\fB::profiler::print\fR ?\fIpattern\fR?
.sp
\fB::profiler::reset\fR ?\fIpattern\fR?
.sp
\fB::profiler::suspend\fR ?\fIpattern\fR?
.sp
\fB::profiler::resume\fR ?\fIpattern\fR?
.sp
\fB::profiler::new-disabled\fR
.sp
\fB::profiler::new-enabled\fR
.sp
\fB::profiler::sortFunctions\fR \fIkey\fR
.sp
.BE
.SH DESCRIPTION
.PP
The \fBprofiler\fR package provides a simple Tcl source code

.TP
\fB::profiler::resume\fR ?\fIpattern\fR?
Resume profiling for all functions matching \fIpattern\fR\&.  If no
pattern is specified, profiling will be resumed for all functions\&.
This command should be invoked after suspending the profiler in the
code\&.
.TP
\fB::profiler::new-disabled\fR
Change the initial profiling state for new procedures\&. Invoking this
command disables profiling for all procedures created after this
command until \fBnew-enabled\fR is invoked\&. Activate profiling of
specific procedures via \fBresume\fR\&.
.TP
\fB::profiler::new-enabled\fR
Change the initial profiling state for new procedures\&. Invoking this
command enables profiling for all procedures created after this
command until \fBnew-disabled\fR is invoked\&. Prevent profiling of
specific procedures via \fBsuspend\fR\&.
.TP
\fB::profiler::sortFunctions\fR \fIkey\fR
Return a list of functions sorted by a particular profiling statistic\&.
Supported values for \fIkey\fR are: \fBcalls\fR,
\fBexclusiveTime\fR, \fBcompileTime\fR, \fBnonCompileTime\fR,
\fBtotalRuntime\fR, \fBavgExclusiveTime\fR, and
\fBavgRuntime\fR\&.  The return result is a list of lists, where each
sublist consists of a function name and the value of \fIkey\fR for

'\"
'\" Generated from file 'matrix\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2002-2013,2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "struct::matrix" n 2\&.0\&.4 tcllib "Tcl Data Structures"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
struct::matrix \- Create and manipulate matrix objects
.SH SYNOPSIS
package require \fBTcl  8\&.2\fR
.sp
package require \fBstruct::matrix  ?2\&.0\&.4?\fR
.sp
\fB::struct::matrix\fR ?\fImatrixName\fR? ?\fB=\fR|\fB:=\fR|\fBas\fR|\fBdeserialize\fR \fIsource\fR?
.sp
\fBmatrixName\fR \fIoption\fR ?\fIarg arg \&.\&.\&.\fR?
.sp
\fImatrixName\fR \fB=\fR \fIsourcematrix\fR
.sp

left-most button in the secondary navigation bar\&.
.SH KEYWORDS
matrix
.SH CATEGORY
Data structures
.SH COPYRIGHT
.nf
Copyright (c) 2002-2013,2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>

.fi

'\"
'\" Generated from file 'matrix1\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2002,2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "struct::matrix_v1" n 1\&.2\&.2 tcllib "Tcl Data Structures"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

..
.BS
.SH NAME
struct::matrix_v1 \- Create and manipulate matrix objects
.SH SYNOPSIS
package require \fBTcl  8\&.2\fR
.sp
package require \fBstruct::matrix  ?1\&.2\&.2?\fR
.sp
\fBmatrixName\fR \fIoption\fR ?\fIarg arg \&.\&.\&.\fR?
.sp
\fImatrixName\fR \fBadd column\fR ?\fIvalues\fR?
.sp
\fImatrixName\fR \fBadd row\fR ?\fIvalues\fR?
.sp

left-most button in the secondary navigation bar\&.
.SH KEYWORDS
matrix
.SH CATEGORY
Data structures
.SH COPYRIGHT
.nf
Copyright (c) 2002,2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>

.fi

'\"
'\" Generated from file 'halfpipe\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2009, 2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>
'\"
.TH "tcl::chan::halfpipe" n 1\&.0\&.1 tcllib "Reflected/virtual channel support"
.\" The -*- nroff -*- definitions below are for supplemental macros used
.\" in Tcl/Tk manual entries.
.\"
.\" .AP type name in/out ?indent?
.\"	Start paragraph describing an argument to a library procedure.
.\"	type is type of argument (int, etc.), in/out is either "in", "out",
.\"	or "in/out" to describe whether procedure reads or modifies arg,

.SH SYNOPSIS
package require \fBTcl  8\&.5\fR
.sp
package require \fBTclOO \fR
.sp
package require \fBtcl::chan::events  ?1?\fR
.sp
package require \fBtcl::chan::halfpipe  ?1\&.0\&.1?\fR


.sp
\fB::tcl::chan::halfpipe\fR ?\fB-option\fR \fIvalue\fR\&.\&.\&.?
.sp
\fIobjectCmd\fR \fBput\fR \fIbytes\fR
.sp
.BE
.SH DESCRIPTION

left-most button in the secondary navigation bar\&.
.SH KEYWORDS
callbacks, fifo, in-memory channel, reflected channel, tip 219, virtual channel
.SH CATEGORY
Channels
.SH COPYRIGHT
.nf
Copyright (c) 2009, 2019 Andreas Kupries <andreas_kupries@users\&.sourceforge\&.net>

.fi

&#124; <a href="../../../toc.html">Table Of Contents</a>
&#124; <a href="../../../../index.html">Keyword Index</a>
&#124; <a href="../../../../toc0.html">Categories</a>
&#124; <a href="../../../../toc1.html">Modules</a>
&#124; <a href="../../../../toc2.html">Applications</a>
 ] <hr>
<div class="doctools">
<h1 class="doctools_title">blowfish(n) 1.0.5 tcllib &quot;Blowfish Block Cipher&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>blowfish - Implementation of the Blowfish block cipher</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.4</b></li>
<li>package require <b class="pkgname">blowfish <span class="opt">?1.0.5?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::blowfish::blowfish</b> <span class="opt">?<i class="arg">-mode [ecb|cbc]</i>?</span> <span class="opt">?<i class="arg">-dir [encrypt|decrypt]</i>?</span> <i class="arg">-key keydata</i> <span class="opt">?<i class="arg">-iv vector</i>?</span> <span class="opt">?<i class="arg">-out channel</i>?</span> <span class="opt">?<i class="arg">-chunksize size</i>?</span> <span class="opt">?<i class="arg">-pad padchar</i>?</span> [ <i class="arg">-in channel</i> | <span class="opt">?<i class="arg">--</i>?</span> <i class="arg">data</i> ]</a></li>
<li><a href="#2"><b class="cmd">::blowfish::Init</b> <i class="arg">mode</i> <i class="arg">keydata</i> <i class="arg">iv</i></a></li>
<li><a href="#3"><b class="cmd">::blowfish::Encrypt</b> <i class="arg">Key</i> <i class="arg">data</i></a></li>
<li><a href="#4"><b class="cmd">::blowfish::Decrypt</b> <i class="arg">Key</i> <i class="arg">data</i></a></li>
<li><a href="#5"><b class="cmd">::blowfish::Reset</b> <i class="arg">Key</i> <i class="arg">iv</i></a></li>

&#124; <a href="../../../toc.html">Table Of Contents</a>
&#124; <a href="../../../../index.html">Keyword Index</a>
&#124; <a href="../../../../toc0.html">Categories</a>
&#124; <a href="../../../../toc1.html">Modules</a>
&#124; <a href="../../../../toc2.html">Applications</a>
 ] <hr>
<div class="doctools">
<h1 class="doctools_title">clay(n) 0.8.6 tcllib &quot;Clay Framework&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>clay - A minimalist framework for large scale OO Projects</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<li><a href="#6">proc <b class="cmd">clay::dynamic_arguments</b> <i class="arg">ensemble</i> <i class="arg">method</i> <i class="arg">arglist</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#7">proc <b class="cmd">clay::dynamic_wrongargs_message</b> <i class="arg">arglist</i></a></li>
<li><a href="#8">proc <b class="cmd">clay::is_dict</b> <i class="arg">d</i></a></li>
<li><a href="#9">proc <b class="cmd">clay::is_null</b> <i class="arg">value</i></a></li>
<li><a href="#10">proc <b class="cmd">clay::leaf</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#11">proc <b class="cmd">clay::K</b> <i class="arg">a</i> <i class="arg">b</i></a></li>
<li><a href="#12">proc <b class="cmd">clay::noop</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#13">proc <b class="cmd">clay::cleanup</b></a></li>
<li><a href="#14">proc <b class="cmd">clay::object_create</b> <i class="arg">objname</i> <span class="opt">?<i class="arg">class</i> <b class="const"></b>?</span></a></li>
<li><a href="#15">proc <b class="cmd">clay::object_rename</b> <i class="arg">object</i> <i class="arg">newname</i></a></li>
<li><a href="#16">proc <b class="cmd">clay::object_destroy</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#17">proc <b class="cmd">clay::path</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#18">proc <b class="cmd">clay::putb</b> <span class="opt">?<i class="arg">map</i>?</span> <i class="arg">text</i></a></li>
<li><a href="#19">proc <b class="cmd">clay::script_path</b></a></li>
<li><a href="#20">proc <b class="cmd">clay::NSNormalize</b> <i class="arg">qualname</i></a></li>
<li><a href="#21">proc <b class="cmd">clay::uuid_generate</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#22">proc <b class="cmd">clay::uuid::generate_tcl_machinfo</b></a></li>
<li><a href="#23">proc <b class="cmd">clay::uuid::tostring</b> <i class="arg">uuid</i></a></li>
<li><a href="#24">proc <b class="cmd">clay::uuid::fromstring</b> <i class="arg">uuid</i></a></li>
<li><a href="#25">proc <b class="cmd">clay::uuid::equal</b> <i class="arg">left</i> <i class="arg">right</i></a></li>
<li><a href="#26">proc <b class="cmd">clay::uuid</b> <i class="arg">cmd</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#27">proc <b class="cmd">clay::tree::sanitize</b> <i class="arg">dict</i></a></li>
<li><a href="#28">proc <b class="cmd">clay::tree::_sanitizeb</b> <i class="arg">path</i> <i class="arg">varname</i> <i class="arg">dict</i></a></li>
<li><a href="#29">proc <b class="cmd">clay::tree::storage</b> <i class="arg">rawpath</i></a></li>
<li><a href="#30">proc <b class="cmd">clay::tree::dictset</b> <i class="arg">varname</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#31">proc <b class="cmd">clay::tree::dictmerge</b> <i class="arg">varname</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#32">proc <b class="cmd">clay::tree::merge</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#33">proc <b class="cmd">dictargs::proc</b> <i class="arg">name</i> <i class="arg">argspec</i> <i class="arg">body</i></a></li>
<li><a href="#34">proc <b class="cmd">dictargs::method</b> <i class="arg">name</i> <i class="arg">argspec</i> <i class="arg">body</i></a></li>
<li><a href="#35">proc <b class="cmd">clay::dialect::Push</b> <i class="arg">class</i></a></li>
<li><a href="#36">proc <b class="cmd">clay::dialect::Peek</b></a></li>




<li><a href="#37">proc <b class="cmd">clay::dialect::Pop</b></a></li>
<li><a href="#38">proc <b class="cmd">clay::dialect::create</b> <i class="arg">name</i> <span class="opt">?<i class="arg">parent</i> <b class="const"></b>?</span></a></li>
<li><a href="#39">proc <b class="cmd">clay::dialect::NSNormalize</b> <i class="arg">namespace</i> <i class="arg">qualname</i></a></li>
<li><a href="#40">proc <b class="cmd">clay::dialect::DefineThunk</b> <i class="arg">target</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#41">proc <b class="cmd">clay::dialect::Canonical</b> <i class="arg">namespace</i> <i class="arg">NSpace</i> <i class="arg">class</i></a></li>
<li><a href="#42">proc <b class="cmd">clay::dialect::Define</b> <i class="arg">namespace</i> <i class="arg">class</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#43">proc <b class="cmd">clay::dialect::Aliases</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#44">proc <b class="cmd">clay::dialect::SuperClass</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#45">proc <b class="cmd">clay::dynamic_methods</b> <i class="arg">class</i></a></li>
<li><a href="#46">proc <b class="cmd">clay::dynamic_methods_class</b> <i class="arg">thisclass</i></a></li>
<li><a href="#47">proc <b class="cmd">clay::define::Array</b> <i class="arg">name</i> <span class="opt">?<i class="arg">values</i> <b class="const"></b>?</span></a></li>
<li><a href="#48">proc <b class="cmd">clay::define::Delegate</b> <i class="arg">name</i> <i class="arg">info</i></a></li>
<li><a href="#49">proc <b class="cmd">clay::define::constructor</b> <i class="arg">arglist</i> <i class="arg">rawbody</i></a></li>
<li><a href="#50">proc <b class="cmd">clay::define::Class_Method</b> <i class="arg">name</i> <i class="arg">arglist</i> <i class="arg">body</i></a></li>
<li><a href="#51">proc <b class="cmd">clay::define::class_method</b> <i class="arg">name</i> <i class="arg">arglist</i> <i class="arg">body</i></a></li>
<li><a href="#52">proc <b class="cmd">clay::define::clay</b> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#53">proc <b class="cmd">clay::define::destructor</b> <i class="arg">rawbody</i></a></li>
<li><a href="#54">proc <b class="cmd">clay::define::Dict</b> <i class="arg">name</i> <span class="opt">?<i class="arg">values</i> <b class="const"></b>?</span></a></li>
<li><a href="#55">proc <b class="cmd">clay::define::Option</b> <i class="arg">name</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#56">proc <b class="cmd">clay::define::Method</b> <i class="arg">name</i> <i class="arg">argstyle</i> <i class="arg">argspec</i> <i class="arg">body</i></a></li>
<li><a href="#57">proc <b class="cmd">clay::define::Option_Class</b> <i class="arg">name</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#58">proc <b class="cmd">clay::define::Variable</b> <i class="arg">name</i> <span class="opt">?<i class="arg">default</i> <b class="const"></b>?</span></a></li>
<li><a href="#59">proc <b class="cmd">clay::ensemble_methodbody</b> <i class="arg">ensemble</i> <i class="arg">einfo</i></a></li>
<li><a href="#60">proc <b class="cmd">clay::define::Ensemble</b> <i class="arg">rawmethod</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>




<li><a href="#61">proc <b class="cmd">clay::event::cancel</b> <i class="arg">self</i> <span class="opt">?<i class="arg">task</i> <b class="const">*</b>?</span></a></li>
<li><a href="#62">proc <b class="cmd">clay::event::generate</b> <i class="arg">self</i> <i class="arg">event</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#63">proc <b class="cmd">clay::event::nextid</b></a></li>
<li><a href="#64">proc <b class="cmd">clay::event::Notification_list</b> <i class="arg">self</i> <i class="arg">event</i> <span class="opt">?<i class="arg">stackvar</i> <b class="const"></b>?</span></a></li>
<li><a href="#65">proc <b class="cmd">clay::event::notify</b> <i class="arg">rcpt</i> <i class="arg">sender</i> <i class="arg">event</i> <i class="arg">eventinfo</i></a></li>
<li><a href="#66">proc <b class="cmd">clay::event::process</b> <i class="arg">self</i> <i class="arg">handle</i> <i class="arg">script</i></a></li>
<li><a href="#67">proc <b class="cmd">clay::event::schedule</b> <i class="arg">self</i> <i class="arg">handle</i> <i class="arg">interval</i> <i class="arg">script</i></a></li>
<li><a href="#68">proc <b class="cmd">clay::event::subscribe</b> <i class="arg">self</i> <i class="arg">who</i> <i class="arg">event</i></a></li>
<li><a href="#69">proc <b class="cmd">clay::event::unsubscribe</b> <i class="arg">self</i> <span class="opt">?<i class="arg">args</i>?</span></a></li>
<li><a href="#70">proc <b class="cmd">clay::singleton</b> <i class="arg">name</i> <i class="arg">script</i></a></li>
<li><a href="#71">method <b class="cmd">clay ancestors</b></a></li>
<li><a href="#72">method <b class="cmd">clay dump</b></a></li>
<li><a href="#73">method <b class="cmd">clay find</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#74">method <b class="cmd">clay get</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#75">method <b class="cmd">clay GET</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#76">method <b class="cmd">clay merge</b> <i class="arg">dict</i> <span class="opt">?<b class="option">dict...</b>?</span></a></li>
<li><a href="#77">method <b class="cmd">clay replace</b> <i class="arg">dictionary</i></a></li>
<li><a href="#78">method <b class="cmd">clay search</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#79">method <b class="cmd">clay set</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span> <i class="arg">value</i></a></li>
<li><a href="#80">method <b class="cmd">clay ancestors</b></a></li>
<li><a href="#81">method <b class="cmd">clay cache</b> <i class="arg">path</i> <i class="arg">value</i></a></li>
<li><a href="#82">method <b class="cmd">clay cget</b> <i class="arg">field</i></a></li>
<li><a href="#83">method <b class="cmd">clay delegate</b> <span class="opt">?<i class="arg">stub</i>?</span> <span class="opt">?<i class="arg">object</i>?</span></a></li>
<li><a href="#84">method <b class="cmd">clay dump</b></a></li>
<li><a href="#85">method <b class="cmd">clay ensemble_map</b></a></li>
<li><a href="#86">method <b class="cmd">clay eval</b> <i class="arg">script</i></a></li>
<li><a href="#87">method <b class="cmd">clay evolve</b></a></li>
<li><a href="#88">method <b class="cmd">clay exists</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#89">method <b class="cmd">clay flush</b></a></li>
<li><a href="#90">method <b class="cmd">clay forward</b> <i class="arg">method</i> <i class="arg">object</i></a></li>
<li><a href="#91">method <b class="cmd">clay get</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#92">method <b class="cmd">clay leaf</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#93">method <b class="cmd">clay merge</b> <i class="arg">dict</i> <span class="opt">?<b class="option">dict...</b>?</span></a></li>
<li><a href="#94">method <b class="cmd">clay mixin</b> <i class="arg">class</i> <span class="opt">?<b class="option">class...</b>?</span></a></li>
<li><a href="#95">method <b class="cmd">clay mixinmap</b> <span class="opt">?<i class="arg">stub</i>?</span> <span class="opt">?<i class="arg">classes</i>?</span></a></li>
<li><a href="#96">method <b class="cmd">clay provenance</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></li>
<li><a href="#97">method <b class="cmd">clay replace</b> <i class="arg">dictionary</i></a></li>
<li><a href="#98">method <b class="cmd">clay search</b> <i class="arg">path</i> <i class="arg">valuevar</i> <i class="arg">isleafvar</i></a></li>
<li><a href="#99">method <b class="cmd">clay source</b> <i class="arg">filename</i></a></li>
<li><a href="#100">method <b class="cmd">clay set</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span> <i class="arg">value</i></a></li>
<li><a href="#101">method <b class="cmd">InitializePublic</b></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>Clay introduces a method ensemble to both <b class="class">oo::class</b> and <b class="class">oo::object</b> called
clay. This ensemble handles all of the high level interactions within the framework.
Clay stores structured data. Clan manages method delegation. Clay has facilities to

<dt><a name="11">proc <b class="cmd">clay::K</b> <i class="arg">a</i> <i class="arg">b</i></a></dt>
<dd></dd>
<dt><a name="12">proc <b class="cmd">clay::noop</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Perform a noop. Useful in prototyping for commenting out blocks
 of code without actually having to comment them out. It also makes
 a handy default for method delegation if a delegate has not been
 assigned yet.</p></dd>
<dt><a name="13">proc <b class="cmd">clay::cleanup</b></a></dt>
<dd><p>Process the queue of objects to be destroyed</p></dd>
<dt><a name="14">proc <b class="cmd">clay::object_create</b> <i class="arg">objname</i> <span class="opt">?<i class="arg">class</i> <b class="const"></b>?</span></a></dt>
<dd></dd>
<dt><a name="15">proc <b class="cmd">clay::object_rename</b> <i class="arg">object</i> <i class="arg">newname</i></a></dt>
<dd></dd>
<dt><a name="16">proc <b class="cmd">clay::object_destroy</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Mark an objects for destruction on the next cleanup</p></dd>
<dt><a name="17">proc <b class="cmd">clay::path</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="18">proc <b class="cmd">clay::putb</b> <span class="opt">?<i class="arg">map</i>?</span> <i class="arg">text</i></a></dt>
<dd><p>Append a line of text to a variable. Optionally apply a string mapping.</p></dd>
<dt><a name="19">proc <b class="cmd">clay::script_path</b></a></dt>
<dd></dd>
<dt><a name="20">proc <b class="cmd">clay::NSNormalize</b> <i class="arg">qualname</i></a></dt>
<dd></dd>
<dt><a name="21">proc <b class="cmd">clay::uuid_generate</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="22">proc <b class="cmd">clay::uuid::generate_tcl_machinfo</b></a></dt>
<dd></dd>
<dt><a name="23">proc <b class="cmd">clay::uuid::tostring</b> <i class="arg">uuid</i></a></dt>
<dd></dd>
<dt><a name="24">proc <b class="cmd">clay::uuid::fromstring</b> <i class="arg">uuid</i></a></dt>
<dd><p>Convert a string representation of a uuid into its binary format.</p></dd>
<dt><a name="25">proc <b class="cmd">clay::uuid::equal</b> <i class="arg">left</i> <i class="arg">right</i></a></dt>
<dd><p>Compare two uuids for equality.</p></dd>
<dt><a name="26">proc <b class="cmd">clay::uuid</b> <i class="arg">cmd</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>uuid generate -&gt; string rep of a new uuid
 uuid equal uuid1 uuid2</p></dd>
<dt><a name="27">proc <b class="cmd">clay::tree::sanitize</b> <i class="arg">dict</i></a></dt>
<dd><p>Output a dictionary removing any . entries added by <b class="function">clay::tree::merge</b></p></dd>
<dt><a name="28">proc <b class="cmd">clay::tree::_sanitizeb</b> <i class="arg">path</i> <i class="arg">varname</i> <i class="arg">dict</i></a></dt>
<dd><p>Helper function for ::clay::tree::sanitize
 Formats the string representation for a dictionary element within
 a human readable stream of lines, and determines if it needs to call itself
 with further indentation to express a sub-branch</p></dd>
<dt><a name="29">proc <b class="cmd">clay::tree::storage</b> <i class="arg">rawpath</i></a></dt>
<dd><p>Return the path as a storage path for clay::tree
 with all branch terminators removed.
 This command will also break arguments up if they
 contain /.</p>
<p>Example:</p>
<pre class="doctools_example"> &gt; clay::tree::storage {foo bar baz bang}
 foo bar baz bang
 &gt; clay::tree::storage {foo bar baz bang/}
 foo bar baz bang
 &gt; clay::tree::storage {foo bar baz bang:}
 foo bar baz bang:
 &gt; clay::tree::storage {foo/bar/baz bang:}
 foo bar baz bang:
 &gt; clay::tree::storage {foo/bar/baz/bang}
 foo bar baz bang
</pre>
</dd>
<dt><a name="30">proc <b class="cmd">clay::tree::dictset</b> <i class="arg">varname</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Set an element with a recursive dictionary,
 marking all branches on the way down to the
 final element.
 If the value does not exists in the nested dictionary
 it is added as a leaf. If the value already exists as a branch
 the value given is merged if the value is a valid dict. If the
 incoming value is not a valid dict, the value overrides the value
 stored, and the value is treated as a leaf from then on.</p>
<p>Example:</p>
<pre class="doctools_example"> &gt; set r {}
 &gt; ::clay::tree::dictset r option color default Green
 . {} option {. {} color {. {} default Green}}
 &gt; ::clay::tree::dictset r option {Something not dictlike}
 . {} option {Something not dictlike}
 # Note that if the value is not a dict, and you try to force it to be
 # an error with be thrown on the merge
 &gt; ::clay::tree::dictset r option color default Blue
 missing value to go with key
</pre>
</dd>
<dt><a name="31">proc <b class="cmd">clay::tree::dictmerge</b> <i class="arg">varname</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>A recursive form of dict merge, intended for modifying variables in place.</p>
<p>Example:</p>
<pre class="doctools_example"> &gt; set mydict {sub/ {sub/ {description {a block of text}}}}
 &gt; ::clay::tree::dictmerge mydict {sub/ {sub/ {field {another block of text}}}}]
 &gt; clay::tree::print $mydict
 sub/ {
   sub/ {
     description {a block of text}
     field {another block of text}
   }
 }
</pre>
</dd>
<dt><a name="32">proc <b class="cmd">clay::tree::merge</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>A recursive form of dict merge</p>
<p>A routine to recursively dig through dicts and merge
 adapted from http://stevehavelka.com/tcl-dict-operation-nested-merge/</p>
<p>Example:</p>
<pre class="doctools_example"> &gt; set mydict {sub/ {sub/ {description {a block of text}}}}
 &gt; set odict [clay::tree::merge $mydict {sub/ {sub/ {field {another block of text}}}}]
 &gt; clay::tree::print $odict
 sub/ {
   sub/ {
     description {a block of text}
     field {another block of text}
   }
 }
</pre>
</dd>
<dt><a name="33">proc <b class="cmd">dictargs::proc</b> <i class="arg">name</i> <i class="arg">argspec</i> <i class="arg">body</i></a></dt>
<dd><p>Named Procedures as new command</p></dd>
<dt><a name="34">proc <b class="cmd">dictargs::method</b> <i class="arg">name</i> <i class="arg">argspec</i> <i class="arg">body</i></a></dt>
<dd></dd>
<dt><a name="35">proc <b class="cmd">clay::dialect::Push</b> <i class="arg">class</i></a></dt>
<dd></dd>
<dt><a name="36">proc <b class="cmd">clay::dialect::Peek</b></a></dt>
<dd></dd>
<dt><a name="37">proc <b class="cmd">clay::dialect::Pop</b></a></dt>
<dd></dd>
<dt><a name="38">proc <b class="cmd">clay::dialect::create</b> <i class="arg">name</i> <span class="opt">?<i class="arg">parent</i> <b class="const"></b>?</span></a></dt>
<dd><p>This proc will generate a namespace, a &quot;mother of all classes&quot;, and a
 rudimentary set of policies for this dialect.</p></dd>
<dt><a name="39">proc <b class="cmd">clay::dialect::NSNormalize</b> <i class="arg">namespace</i> <i class="arg">qualname</i></a></dt>
<dd><p>Support commands; not intended to be called directly.</p></dd>
<dt><a name="40">proc <b class="cmd">clay::dialect::DefineThunk</b> <i class="arg">target</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="41">proc <b class="cmd">clay::dialect::Canonical</b> <i class="arg">namespace</i> <i class="arg">NSpace</i> <i class="arg">class</i></a></dt>
<dd></dd>
<dt><a name="42">proc <b class="cmd">clay::dialect::Define</b> <i class="arg">namespace</i> <i class="arg">class</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Implementation of the languages' define command</p></dd>
<dt><a name="43">proc <b class="cmd">clay::dialect::Aliases</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="44">proc <b class="cmd">clay::dialect::SuperClass</b> <i class="arg">namespace</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="45">proc <b class="cmd">clay::dynamic_methods</b> <i class="arg">class</i></a></dt>
<dd></dd>
<dt><a name="46">proc <b class="cmd">clay::dynamic_methods_class</b> <i class="arg">thisclass</i></a></dt>
<dd></dd>
<dt><a name="47">proc <b class="cmd">clay::define::Array</b> <i class="arg">name</i> <span class="opt">?<i class="arg">values</i> <b class="const"></b>?</span></a></dt>
<dd><p>New OO Keywords for clay</p></dd>
<dt><a name="48">proc <b class="cmd">clay::define::Delegate</b> <i class="arg">name</i> <i class="arg">info</i></a></dt>
<dd><p>An annotation that objects of this class interact with delegated
 methods. The annotation is intended to be a dictionary, and the
 only reserved key is <em>description</em>, a human readable description.</p></dd>
<dt><a name="49">proc <b class="cmd">clay::define::constructor</b> <i class="arg">arglist</i> <i class="arg">rawbody</i></a></dt>
<dd></dd>
<dt><a name="50">proc <b class="cmd">clay::define::Class_Method</b> <i class="arg">name</i> <i class="arg">arglist</i> <i class="arg">body</i></a></dt>
<dd><p>Specify the a method for the class object itself, instead of for objects of the class</p></dd>
<dt><a name="51">proc <b class="cmd">clay::define::class_method</b> <i class="arg">name</i> <i class="arg">arglist</i> <i class="arg">body</i></a></dt>
<dd><p>And alias to the new Class_Method keyword</p></dd>
<dt><a name="52">proc <b class="cmd">clay::define::clay</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>
<dt><a name="53">proc <b class="cmd">clay::define::destructor</b> <i class="arg">rawbody</i></a></dt>
<dd></dd>
<dt><a name="54">proc <b class="cmd">clay::define::Dict</b> <i class="arg">name</i> <span class="opt">?<i class="arg">values</i> <b class="const"></b>?</span></a></dt>
<dd></dd>
<dt><a name="55">proc <b class="cmd">clay::define::Option</b> <i class="arg">name</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Define an option for the class</p></dd>
<dt><a name="56">proc <b class="cmd">clay::define::Method</b> <i class="arg">name</i> <i class="arg">argstyle</i> <i class="arg">argspec</i> <i class="arg">body</i></a></dt>
<dd></dd>
<dt><a name="57">proc <b class="cmd">clay::define::Option_Class</b> <i class="arg">name</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Define a class of options
 All field / value pairs will be be inherited by an option that
 specify <em>name</em> as it class field.</p></dd>
<dt><a name="58">proc <b class="cmd">clay::define::Variable</b> <i class="arg">name</i> <span class="opt">?<i class="arg">default</i> <b class="const"></b>?</span></a></dt>
<dd><p>This keyword can also be expressed:</p>
<pre class="doctools_example">property variable NAME {default DEFAULT}</pre>
<p>Variables registered in the variable property are also initialized
    (if missing) when the object changes class via the <em>morph</em> method.</p></dd>
<dt><a name="59">proc <b class="cmd">clay::ensemble_methodbody</b> <i class="arg">ensemble</i> <i class="arg">einfo</i></a></dt>
<dd><p>Produce the body of an ensemble's public dispatch method
 ensemble is the name of the the ensemble.
 einfo is a dictionary of methods for the ensemble, and each value is a script
 to execute on dispatch</p>
<p>Example:</p>
<pre class="doctools_example"> ::clay::ensemble_methodbody foo {
   bar {tailcall my Foo_bar {*}$args}
   baz {tailcall my Foo_baz {*}$args}
   clock {return [clock seconds]}
   default {puts &quot;You gave me $method&quot;}
 }
</pre>
</dd>
<dt><a name="60">proc <b class="cmd">clay::define::Ensemble</b> <i class="arg">rawmethod</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd></dd>








<dt><a name="61">proc <b class="cmd">clay::event::cancel</b> <i class="arg">self</i> <span class="opt">?<i class="arg">task</i> <b class="const">*</b>?</span></a></dt>
<dd><p>Cancel a scheduled event</p></dd>
<dt><a name="62">proc <b class="cmd">clay::event::generate</b> <i class="arg">self</i> <i class="arg">event</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Generate an event
    Adds a subscription mechanism for objects
    to see who has recieved this event and prevent
    spamming or infinite recursion</p></dd>

<dd><p>Evaluate an event script in the global namespace</p></dd>
<dt><a name="67">proc <b class="cmd">clay::event::schedule</b> <i class="arg">self</i> <i class="arg">handle</i> <i class="arg">interval</i> <i class="arg">script</i></a></dt>
<dd><p>Schedule an event to occur later</p></dd>
<dt><a name="68">proc <b class="cmd">clay::event::subscribe</b> <i class="arg">self</i> <i class="arg">who</i> <i class="arg">event</i></a></dt>
<dd><p>Subscribe an object to an event pattern</p></dd>
<dt><a name="69">proc <b class="cmd">clay::event::unsubscribe</b> <i class="arg">self</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Unsubscribe an object from an event pattern</p></dd>
<dt><a name="70">proc <b class="cmd">clay::singleton</b> <i class="arg">name</i> <i class="arg">script</i></a></dt>
<dd><p>An object which is intended to be it's own class.</p></dd>
</dl>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">Classes</a></h2>
<div id="subsection4" class="doctools_subsection"><h3><a name="subsection4">Class  clay::class</a></h3>
<p><b class="class">Methods</b></p>
<dl class="doctools_definitions">
<dt><a name="71">method <b class="cmd">clay ancestors</b></a></dt>
<dd><p>Return this class and all ancestors in search order.</p></dd>
<dt><a name="72">method <b class="cmd">clay dump</b></a></dt>
<dd><p>Return a complete dump of this object's clay data, but only this object's clay data.</p></dd>
<dt><a name="73">method <b class="cmd">clay find</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Pull a chunk of data from the clay system. If the last element of <em>path</em> is a branch,
     returns a recursive merge of all data from this object and it's constituent classes of the data in that branch.
     If the last element is a leaf, search this object for a matching leaf, or search all  constituent classes for a matching
     leaf and return the first value found.
     If no value is found, returns an empty string.
     If a branch is returned the topmost . entry is omitted.</p></dd>
<dt><a name="74">method <b class="cmd">clay get</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Pull a chunk of data from the class's clay system.
     If no value is found, returns an empty string.
     If a branch is returned the topmost . entry is omitted.</p></dd>
<dt><a name="75">method <b class="cmd">clay GET</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Pull a chunk of data from the class's clay system.
     If no value is found, returns an empty string.</p></dd>
<dt><a name="76">method <b class="cmd">clay merge</b> <i class="arg">dict</i> <span class="opt">?<b class="option">dict...</b>?</span></a></dt>
<dd><p>Recursively merge the dictionaries given into the object's local clay storage.</p></dd>
<dt><a name="77">method <b class="cmd">clay replace</b> <i class="arg">dictionary</i></a></dt>
<dd><p>Replace the contents of the internal clay storage with the dictionary given.</p></dd>
<dt><a name="78">method <b class="cmd">clay search</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Return the first matching value for the path in either this class's clay data or one of its ancestors</p></dd>
<dt><a name="79">method <b class="cmd">clay set</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span> <i class="arg">value</i></a></dt>
<dd><p>Merge the conents of <b class="const">value</b> with the object's clay storage at <b class="const">path</b>.</p></dd>
</dl>
</div>
<div id="subsection5" class="doctools_subsection"><h3><a name="subsection5">Class  clay::object</a></h3>
<p>clay::object
 This class is inherited by all classes that have options.</p>
<p><b class="class">Methods</b></p>
<dl class="doctools_definitions">
<dt><a name="80">method <b class="cmd">clay ancestors</b></a></dt>
<dd><p>Return the class this object belongs to, all classes mixed into this object, and all ancestors of those classes in search order.</p></dd>
<dt><a name="81">method <b class="cmd">clay cache</b> <i class="arg">path</i> <i class="arg">value</i></a></dt>
<dd><p>Store VALUE in such a way that request in SEARCH for PATH will always return it until the cache is flushed</p></dd>
<dt><a name="82">method <b class="cmd">clay cget</b> <i class="arg">field</i></a></dt>
<dd><p>Pull a value from either the object's clay structure or one of its constituent classes that matches the field name.
 The order of search us:</p>
<p>1. The as a value in local dict variable config</p>
<p>2. The as a value in local dict variable clay</p>
<p>3. As a leaf in any ancestor as a root of the clay tree</p>
<p>4. As a leaf in any ancestor as <b class="const">const</b> <em>field</em></p>
<p>5. As a leaf in any ancestor as <b class="const">option</b> <em>field</em> <b class="const">default</b></p></dd>
<dt><a name="83">method <b class="cmd">clay delegate</b> <span class="opt">?<i class="arg">stub</i>?</span> <span class="opt">?<i class="arg">object</i>?</span></a></dt>
<dd><p>Introspect or control method delegation. With no arguments, the method will return a
 key/value list of stubs and objects. With just the <i class="arg">stub</i> argument, the method will
 return the object (if any) attached to the stub. With a <i class="arg">stub</i> and an <i class="arg">object</i>
 this command will forward all calls to the method <i class="arg">stub</i> to the <i class="arg">object</i>.</p></dd>
<dt><a name="84">method <b class="cmd">clay dump</b></a></dt>
<dd><p>Return a complete dump of this object's clay data, as well as the data from all constituent classes recursively blended in.</p></dd>
<dt><a name="85">method <b class="cmd">clay ensemble_map</b></a></dt>
<dd><p>Return a dictionary describing the method ensembles to be assembled for this object</p></dd>
<dt><a name="86">method <b class="cmd">clay eval</b> <i class="arg">script</i></a></dt>
<dd><p>Evaluated a script in the namespace of this object</p></dd>
<dt><a name="87">method <b class="cmd">clay evolve</b></a></dt>
<dd><p>Trigger the <b class="method">InitializePublic</b> private method</p></dd>
<dt><a name="88">method <b class="cmd">clay exists</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Returns 1 if <em>path</em> exists in either the object's clay data. Values greater than one indicate the element exists in one of the object's constituent classes. A value of zero indicates the path could not be found.</p></dd>
<dt><a name="89">method <b class="cmd">clay flush</b></a></dt>
<dd><p>Wipe any caches built by the clay implementation</p></dd>
<dt><a name="90">method <b class="cmd">clay forward</b> <i class="arg">method</i> <i class="arg">object</i></a></dt>
<dd><p>A convenience wrapper for</p>
<pre class="doctools_example">oo::objdefine [self] forward {*}$args</pre>
</dd>
<dt><a name="91">method <b class="cmd">clay get</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Pull a chunk of data from the clay system. If the last element of <em>path</em> is a branch (ends in a slash /),
   returns a recursive merge of all data from this object and it's constituent classes of the data in that branch.
   If the last element is a leaf, search this object for a matching leaf, or search all  constituent classes for a matching
   leaf and return the first value found.
   If no value is found, returns an empty string.</p></dd>
<dt><a name="92">method <b class="cmd">clay leaf</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>A modified get which is tailored to pull only leaf elements</p></dd>
<dt><a name="93">method <b class="cmd">clay merge</b> <i class="arg">dict</i> <span class="opt">?<b class="option">dict...</b>?</span></a></dt>
<dd><p>Recursively merge the dictionaries given into the object's local clay storage.</p></dd>
<dt><a name="94">method <b class="cmd">clay mixin</b> <i class="arg">class</i> <span class="opt">?<b class="option">class...</b>?</span></a></dt>
<dd><p>Perform [oo::objdefine [self] mixin] on this object, with a few additional rules:
   Prior to the call, for any class was previously mixed in, but not in the new result, execute the script registered to mixin/ unmap-script (if given.)
   For all new classes, that were not present prior to this call, after the native TclOO mixin is invoked, execute the script registered to mixin/ map-script (if given.)
   Fall all classes that are now present and “mixed in”, execute the script registered to mixin/ react-script (if given.)</p></dd>
<dt><a name="95">method <b class="cmd">clay mixinmap</b> <span class="opt">?<i class="arg">stub</i>?</span> <span class="opt">?<i class="arg">classes</i>?</span></a></dt>
<dd><p>With no arguments returns the map of stubs and classes mixed into the current object. When only stub is given,
  returns the classes mixed in on that stub. When stub and classlist given, replace the classes currently on that stub with the given
  classes and invoke clay mixin on the new matrix of mixed in classes.</p></dd>
<dt><a name="96">method <b class="cmd">clay provenance</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span></a></dt>
<dd><p>Return either <b class="const">self</b> if that path exists in the current object, or return the first class (if any) along the clay search path which contains that element.</p></dd>
<dt><a name="97">method <b class="cmd">clay replace</b> <i class="arg">dictionary</i></a></dt>
<dd><p>Replace the contents of the internal clay storage with the dictionary given.</p></dd>
<dt><a name="98">method <b class="cmd">clay search</b> <i class="arg">path</i> <i class="arg">valuevar</i> <i class="arg">isleafvar</i></a></dt>
<dd><p>Return true, and set valuevar to the value and isleafar to true for false if PATH was found in the cache.</p></dd>
<dt><a name="99">method <b class="cmd">clay source</b> <i class="arg">filename</i></a></dt>
<dd><p>Source the given filename within the object's namespace</p></dd>
<dt><a name="100">method <b class="cmd">clay set</b> <i class="arg">path</i> <span class="opt">?<b class="option">path...</b>?</span> <i class="arg">value</i></a></dt>
<dd><p>Merge the conents of <b class="const">value</b> with the object's clay storage at <b class="const">path</b>.</p></dd>
<dt><a name="101">method <b class="cmd">InitializePublic</b></a></dt>
<dd><p>Instantiate variables. Called on object creation and during clay mixin.</p></dd>
</dl>
</div>
</div>
<div id="section4" class="doctools_section"><h2><a name="section4">AUTHORS</a></h2>
<p>Sean Woods <a href="mailto:<[email protected]>">mailto:&lt;[email protected]&gt;</a></p>
</div>

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<h1 class="doctools_title">debug::heartbeat(n) 1.0.1 tcllib &quot;debug narrative&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>debug::heartbeat - debug narrative - heartbeat</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">API</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">debug::heartbeat <span class="opt">?1.0.1?</span></b></li>
<li>package require <b class="pkgname">debug <span class="opt">?1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd"><a href="debug.html">debug</a></b> <b class="method">heartbeat</b> <span class="opt">?<i class="arg">delta</i>?</span></a></li>
</ul>
</div>
</div>

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<div class="doctools">
<h1 class="doctools_title">dns(n) 1.4.1 tcllib &quot;Domain Name Service&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>dns - Tcl Domain Name Service Client</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.2</b></li>
<li>package require <b class="pkgname">dns <span class="opt">?1.4.1?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::dns::resolve</b> <i class="arg">query</i> <span class="opt">?<i class="arg">options</i>?</span></a></li>
<li><a href="#2"><b class="cmd">::dns::configure</b> <span class="opt">?<i class="arg">options</i>?</span></a></li>
<li><a href="#3"><b class="cmd">::dns::name</b> <i class="arg">token</i></a></li>
<li><a href="#4"><b class="cmd">::dns::address</b> <i class="arg">token</i></a></li>
<li><a href="#5"><b class="cmd">::dns::cname</b> <i class="arg">token</i></a></li>

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<h1 class="doctools_title">httpd(n) 4.3.4 tcllib &quot;Tcl Web Server&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>httpd - A TclOO and coroutine based web server</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

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<div class="doctools">
<h1 class="doctools_title">markdown(n) 1.1.1 tcllib &quot;Markdown to HTML Converter&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>markdown - Converts Markdown text to HTML</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.5</b></li>
<li>package require <b class="pkgname">Markdown 1.1.1</b></li>
<li>package require <b class="pkgname">textutil <span class="opt">?0.8?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::Markdown::convert</b> <i class="arg">markdown</i></a></li>
<li><a href="#2"><b class="cmd">::Markdown::register</b> <i class="arg">langspec</i> <i class="arg">converter</i></a></li>
<li><a href="#3"><b class="cmd">::Markdown::get_lang_counter</b></a></li>
<li><a href="#4"><b class="cmd">::Markdown::reset_lang_counter</b></a></li>

<li><a href="#8"><b class="cmd">::math::geometry::h</b> <i class="arg">length</i></a></li>
<li><a href="#9"><b class="cmd">::math::geometry::v</b> <i class="arg">length</i></a></li>
<li><a href="#10"><b class="cmd">::math::geometry::between</b> <i class="arg">point1</i> <i class="arg">point2</i> <i class="arg">s</i></a></li>
<li><a href="#11"><b class="cmd">::math::geometry::octant</b> <i class="arg">point</i></a></li>
<li><a href="#12"><b class="cmd">::math::geometry::rect</b> <i class="arg">nw</i> <i class="arg">se</i></a></li>
<li><a href="#13"><b class="cmd">::math::geometry::nwse</b> <i class="arg">rect</i></a></li>
<li><a href="#14"><b class="cmd">::math::geometry::angle</b> <i class="arg">line</i></a></li>
<li><a href="#15"><b class="cmd">::math::geometry::angleBetween</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></li>
<li><a href="#16"><b class="cmd">::math::geometry::inproduct</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></li>
<li><a href="#17"><b class="cmd">::math::geometry::areaParallellogram</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></li>
<li><a href="#18"><b class="cmd">::math::geometry::calculateDistanceToLine</b> <i class="arg">P</i> <i class="arg">line</i></a></li>
<li><a href="#19"><b class="cmd">::math::geometry::calculateDistanceToLineSegment</b> <i class="arg">P</i> <i class="arg">linesegment</i></a></li>
<li><a href="#20"><b class="cmd">::math::geometry::calculateDistanceToPolyline</b> <i class="arg">P</i> <i class="arg">polyline</i></a></li>
<li><a href="#21"><b class="cmd">::math::geometry::calculateDistanceToPolygon</b> <i class="arg">P</i> <i class="arg">polygon</i></a></li>
<li><a href="#22"><b class="cmd">::math::geometry::findClosestPointOnLine</b> <i class="arg">P</i> <i class="arg">line</i></a></li>
<li><a href="#23"><b class="cmd">::math::geometry::findClosestPointOnLineSegment</b> <i class="arg">P</i> <i class="arg">linesegment</i></a></li>
<li><a href="#24"><b class="cmd">::math::geometry::findClosestPointOnPolyline</b> <i class="arg">P</i> <i class="arg">polyline</i></a></li>
<li><a href="#25"><b class="cmd">::math::geometry::lengthOfPolyline</b> <i class="arg">polyline</i></a></li>
<li><a href="#26"><b class="cmd">::math::geometry::movePointInDirection</b> <i class="arg">P</i> <i class="arg">direction</i> <i class="arg">dist</i></a></li>
<li><a href="#27"><b class="cmd">::math::geometry::lineSegmentsIntersect</b> <i class="arg">linesegment1</i> <i class="arg">linesegment2</i></a></li>
<li><a href="#28"><b class="cmd">::math::geometry::findLineSegmentIntersection</b> <i class="arg">linesegment1</i> <i class="arg">linesegment2</i></a></li>
<li><a href="#29"><b class="cmd">::math::geometry::findLineIntersection</b> <i class="arg">line1</i> <i class="arg">line2</i></a></li>
<li><a href="#30"><b class="cmd">::math::geometry::polylinesIntersect</b> <i class="arg">polyline1</i> <i class="arg">polyline2</i></a></li>
<li><a href="#31"><b class="cmd">::math::geometry::polylinesBoundingIntersect</b> <i class="arg">polyline1</i> <i class="arg">polyline2</i> <i class="arg">granularity</i></a></li>
<li><a href="#32"><b class="cmd">::math::geometry::intervalsOverlap</b> <i class="arg">y1</i> <i class="arg">y2</i> <i class="arg">y3</i> <i class="arg">y4</i> <i class="arg">strict</i></a></li>
<li><a href="#33"><b class="cmd">::math::geometry::rectanglesOverlap</b> <i class="arg">P1</i> <i class="arg">P2</i> <i class="arg">Q1</i> <i class="arg">Q2</i> <i class="arg">strict</i></a></li>
<li><a href="#34"><b class="cmd">::math::geometry::bbox</b> <i class="arg">polyline</i></a></li>
<li><a href="#35"><b class="cmd">::math::geometry::pointInsidePolygon</b> <i class="arg">P</i> <i class="arg">polyline</i></a></li>
<li><a href="#36"><b class="cmd">::math::geometry::pointInsidePolygonAlt</b> <i class="arg">P</i> <i class="arg">polyline</i></a></li>
<li><a href="#37"><b class="cmd">::math::geometry::rectangleInsidePolygon</b> <i class="arg">P1</i> <i class="arg">P2</i> <i class="arg">polyline</i></a></li>
<li><a href="#38"><b class="cmd">::math::geometry::areaPolygon</b> <i class="arg">polygon</i></a></li>
<li><a href="#39"><b class="cmd">::math::geometry::translate</b> <i class="arg">vector</i> <i class="arg">polyline</i></a></li>
<li><a href="#40"><b class="cmd">::math::geometry::rotate</b> <i class="arg">angle</i> <i class="arg">polyline</i></a></li>
<li><a href="#41"><b class="cmd">::math::geometry::reflect</b> <i class="arg">angle</i> <i class="arg">polyline</i></a></li>
<li><a href="#42"><b class="cmd">::math::geometry::degToRad</b> <i class="arg">angle</i></a></li>
<li><a href="#43"><b class="cmd">::math::geometry::radToDeg</b> <i class="arg">angle</i></a></li>
<li><a href="#44"><b class="cmd">::math::geometry::circle</b> <i class="arg">centre</i> <i class="arg">radius</i></a></li>
<li><a href="#45"><b class="cmd">::math::geometry::circleTwoPoints</b> <i class="arg">point1</i> <i class="arg">point2</i></a></li>
<li><a href="#46"><b class="cmd">::math::geometry::pointInsideCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></li>
<li><a href="#47"><b class="cmd">::math::geometry::lineIntersectsCircle</b> <i class="arg">line</i> <i class="arg">circle</i></a></li>
<li><a href="#48"><b class="cmd">::math::geometry::lineSegmentIntersectsCircle</b> <i class="arg">segment</i> <i class="arg">circle</i></a></li>
<li><a href="#49"><b class="cmd">::math::geometry::intersectionLineWithCircle</b> <i class="arg">line</i> <i class="arg">circle</i></a></li>
<li><a href="#50"><b class="cmd">::math::geometry::intersectionCircleWithCircle</b> <i class="arg">circle1</i> <i class="arg">circle2</i></a></li>
<li><a href="#51"><b class="cmd">::math::geometry::tangentLinesToCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">math::geometry</b> package is a collection of functions for
computations and manipulations on two-dimensional geometrical objects,
such as points, lines and polygons.</p>

<dt><a name="14"><b class="cmd">::math::geometry::angle</b> <i class="arg">line</i></a></dt>
<dd><p>Calculate the angle from the positive x-axis to a given line
(in two dimensions only).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">line</i></dt>
<dd><p>Coordinates of the line</p></dd>
</dl></dd>
<dt><a name="15"><b class="cmd">::math::geometry::angleBetween</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></dt>
<dd><p>Calculate the angle between two vectors (in degrees)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">vector1</i></dt>
<dd><p>First vector</p></dd>
<dt>list <i class="arg">vector2</i></dt>
<dd><p>Second vector</p></dd>
</dl></dd>
<dt><a name="16"><b class="cmd">::math::geometry::inproduct</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></dt>
<dd><p>Calculate the inner product of two vectors</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">vector1</i></dt>
<dd><p>First vector</p></dd>
<dt>list <i class="arg">vector2</i></dt>
<dd><p>Second vector</p></dd>
</dl></dd>
<dt><a name="17"><b class="cmd">::math::geometry::areaParallellogram</b> <i class="arg">vector1</i> <i class="arg">vector2</i></a></dt>
<dd><p>Calculate the area of the parallellogram with the two vectors as its sides</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">vector1</i></dt>
<dd><p>First vector</p></dd>
<dt>list <i class="arg">vector2</i></dt>
<dd><p>Second vector</p></dd>
</dl></dd>
<dt><a name="18"><b class="cmd">::math::geometry::calculateDistanceToLine</b> <i class="arg">P</i> <i class="arg">line</i></a></dt>
<dd><p>Calculate the distance of point P to the (infinite) line and return the
result</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">line</i></dt>
<dd><p>List of four numbers, the coordinates of two points
on the line</p></dd>
</dl></dd>
<dt><a name="19"><b class="cmd">::math::geometry::calculateDistanceToLineSegment</b> <i class="arg">P</i> <i class="arg">linesegment</i></a></dt>
<dd><p>Calculate the distance of point P to the (finite) line segment and
return the result.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">linesegment</i></dt>
<dd><p>List of four numbers, the coordinates of the
first and last points of the line segment</p></dd>
</dl></dd>
<dt><a name="20"><b class="cmd">::math::geometry::calculateDistanceToPolyline</b> <i class="arg">P</i> <i class="arg">polyline</i></a></dt>
<dd><p>Calculate the distance of point P to the polyline and
return the result. Note that a polyline needs not to be closed.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>List of numbers, the coordinates of the
vertices of the polyline</p></dd>
</dl></dd>
<dt><a name="21"><b class="cmd">::math::geometry::calculateDistanceToPolygon</b> <i class="arg">P</i> <i class="arg">polygon</i></a></dt>
<dd><p>Calculate the distance of point P to the polygon and
return the result. If the list of coordinates is not closed (first and last
points differ), it is automatically closed.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">polygon</i></dt>
<dd><p>List of numbers, the coordinates of the
vertices of the polygon</p></dd>
</dl></dd>
<dt><a name="22"><b class="cmd">::math::geometry::findClosestPointOnLine</b> <i class="arg">P</i> <i class="arg">line</i></a></dt>
<dd><p>Return the point on a line which is closest to a given point.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">line</i></dt>
<dd><p>List of four numbers, the coordinates of two points
on the line</p></dd>
</dl></dd>
<dt><a name="23"><b class="cmd">::math::geometry::findClosestPointOnLineSegment</b> <i class="arg">P</i> <i class="arg">linesegment</i></a></dt>
<dd><p>Return the point on a <em>line segment</em> which is closest to a given
point.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">linesegment</i></dt>
<dd><p>List of four numbers, the first and last
points on the line segment</p></dd>
</dl></dd>
<dt><a name="24"><b class="cmd">::math::geometry::findClosestPointOnPolyline</b> <i class="arg">P</i> <i class="arg">polyline</i></a></dt>
<dd><p>Return the point on a <em>polyline</em> which is closest to a given
point.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>List of two numbers, the coordinates of the point</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>List of numbers, the vertices of the polyline</p></dd>
</dl></dd>
<dt><a name="25"><b class="cmd">::math::geometry::lengthOfPolyline</b> <i class="arg">polyline</i></a></dt>
<dd><p>Return the length of the <em>polyline</em> (note: it not regarded as a
polygon)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">polyline</i></dt>
<dd><p>List of numbers, the vertices of the polyline</p></dd>
</dl></dd>
<dt><a name="26"><b class="cmd">::math::geometry::movePointInDirection</b> <i class="arg">P</i> <i class="arg">direction</i> <i class="arg">dist</i></a></dt>
<dd><p>Move a point over a given distance in a given direction and return the
new coordinates (in two dimensions only).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>Coordinates of the point to be moved</p></dd>
<dt>double <i class="arg">direction</i></dt>
<dd><p>Direction (in degrees; 0 is to the right, 90
upwards)</p></dd>
<dt>list <i class="arg">dist</i></dt>
<dd><p>Distance over which to move the point</p></dd>
</dl></dd>
<dt><a name="27"><b class="cmd">::math::geometry::lineSegmentsIntersect</b> <i class="arg">linesegment1</i> <i class="arg">linesegment2</i></a></dt>
<dd><p>Check if two line segments intersect or coincide. Returns 1 if that is
the case, 0 otherwise (in two dimensions only). If an endpoint of one segment lies on
the other segment (or is very close to the segment), they are considered to intersect</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">linesegment1</i></dt>
<dd><p>First line segment</p></dd>
<dt>list <i class="arg">linesegment2</i></dt>
<dd><p>Second line segment</p></dd>
</dl></dd>
<dt><a name="28"><b class="cmd">::math::geometry::findLineSegmentIntersection</b> <i class="arg">linesegment1</i> <i class="arg">linesegment2</i></a></dt>
<dd><p>Find the intersection point of two line segments. Return the coordinates
or the keywords &quot;coincident&quot; or &quot;none&quot; if the line segments coincide or
have no points in common (in two dimensions only).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">linesegment1</i></dt>
<dd><p>First line segment</p></dd>
<dt>list <i class="arg">linesegment2</i></dt>
<dd><p>Second line segment</p></dd>
</dl></dd>
<dt><a name="29"><b class="cmd">::math::geometry::findLineIntersection</b> <i class="arg">line1</i> <i class="arg">line2</i></a></dt>
<dd><p>Find the intersection point of two (infinite) lines. Return the coordinates
or the keywords &quot;coincident&quot; or &quot;none&quot; if the lines coincide or
have no points in common (in two dimensions only).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">line1</i></dt>
<dd><p>First line</p></dd>
<dt>list <i class="arg">line2</i></dt>
<dd><p>Second line</p></dd>
</dl>
<p>See section <span class="sectref"><a href="#section3">References</a></span> for details on the algorithm and math behind it.</p></dd>
<dt><a name="30"><b class="cmd">::math::geometry::polylinesIntersect</b> <i class="arg">polyline1</i> <i class="arg">polyline2</i></a></dt>
<dd><p>Check if two polylines intersect or not (in two dimensions only).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">polyline1</i></dt>
<dd><p>First polyline</p></dd>
<dt>list <i class="arg">polyline2</i></dt>
<dd><p>Second polyline</p></dd>
</dl></dd>
<dt><a name="31"><b class="cmd">::math::geometry::polylinesBoundingIntersect</b> <i class="arg">polyline1</i> <i class="arg">polyline2</i> <i class="arg">granularity</i></a></dt>
<dd><p>Check whether two polylines intersect, but reduce
the correctness of the result to the given granularity.
Use this for faster, but weaker, intersection checking.</p>
<p>How it works:</p>
<p>Each polyline is split into a number of smaller polylines,
consisting of granularity points each. If a pair of those smaller
lines' bounding boxes intersect, then this procedure returns 1,
otherwise it returns 0.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">polyline1</i></dt>
<dd><p>First polyline</p></dd>
<dt>list <i class="arg">polyline2</i></dt>
<dd><p>Second polyline</p></dd>
<dt>int <i class="arg">granularity</i></dt>
<dd><p>Number of points in each part (&lt;=1 means check
every edge)</p></dd>
</dl></dd>
<dt><a name="32"><b class="cmd">::math::geometry::intervalsOverlap</b> <i class="arg">y1</i> <i class="arg">y2</i> <i class="arg">y3</i> <i class="arg">y4</i> <i class="arg">strict</i></a></dt>
<dd><p>Check if two intervals overlap.</p>
<dl class="doctools_arguments">
<dt>double <i class="arg">y1,y2</i></dt>
<dd><p>Begin and end of first interval</p></dd>
<dt>double <i class="arg">y3,y4</i></dt>
<dd><p>Begin and end of second interval</p></dd>
<dt>logical <i class="arg">strict</i></dt>
<dd><p>Check for strict or non-strict overlap</p></dd>
</dl></dd>
<dt><a name="33"><b class="cmd">::math::geometry::rectanglesOverlap</b> <i class="arg">P1</i> <i class="arg">P2</i> <i class="arg">Q1</i> <i class="arg">Q2</i> <i class="arg">strict</i></a></dt>
<dd><p>Check if two rectangles overlap.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P1</i></dt>
<dd><p>upper-left corner of the first rectangle</p></dd>
<dt>list <i class="arg">P2</i></dt>
<dd><p>lower-right corner of the first rectangle</p></dd>
<dt>list <i class="arg">Q1</i></dt>
<dd><p>upper-left corner of the second rectangle</p></dd>
<dt>list <i class="arg">Q2</i></dt>
<dd><p>lower-right corner of the second rectangle</p></dd>
<dt>list <i class="arg">strict</i></dt>
<dd><p>choosing strict or non-strict interpretation</p></dd>
</dl></dd>
<dt><a name="34"><b class="cmd">::math::geometry::bbox</b> <i class="arg">polyline</i></a></dt>
<dd><p>Calculate the bounding box of a polyline. Returns a list of four
coordinates: the upper-left and the lower-right corner of the box.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be examined</p></dd>
</dl></dd>
<dt><a name="35"><b class="cmd">::math::geometry::pointInsidePolygon</b> <i class="arg">P</i> <i class="arg">polyline</i></a></dt>
<dd><p>Determine if a point is completely inside a polygon. If the point
touches the polygon, then the point is not completely inside the
polygon.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>Coordinates of the point</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be examined</p></dd>
</dl></dd>
<dt><a name="36"><b class="cmd">::math::geometry::pointInsidePolygonAlt</b> <i class="arg">P</i> <i class="arg">polyline</i></a></dt>
<dd><p>Determine if a point is completely inside a polygon. If the point
touches the polygon, then the point is not completely inside the
polygon. <em>Note:</em> this alternative procedure uses the so-called
winding number to determine this. It handles self-intersecting polygons
in a &quot;natural&quot; way.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P</i></dt>
<dd><p>Coordinates of the point</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be examined</p></dd>
</dl></dd>
<dt><a name="37"><b class="cmd">::math::geometry::rectangleInsidePolygon</b> <i class="arg">P1</i> <i class="arg">P2</i> <i class="arg">polyline</i></a></dt>
<dd><p>Determine if a rectangle is completely inside a polygon. If polygon
touches the rectangle, then the rectangle is not complete inside the
polygon.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">P1</i></dt>
<dd><p>Upper-left corner of the rectangle</p></dd>
<dt>list <i class="arg">P2</i></dt>
<dd><p>Lower-right corner of the rectangle</p></dd>
<dt>list <i class="arg">polygon</i></dt>
<dd><p>The polygon in question</p></dd>
</dl></dd>
<dt><a name="38"><b class="cmd">::math::geometry::areaPolygon</b> <i class="arg">polygon</i></a></dt>
<dd><p>Calculate the area of a polygon.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">polygon</i></dt>
<dd><p>The polygon in question</p></dd>
</dl></dd>
<dt><a name="39"><b class="cmd">::math::geometry::translate</b> <i class="arg">vector</i> <i class="arg">polyline</i></a></dt>
<dd><p>Translate a polyline over a given vector</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">vector</i></dt>
<dd><p>Translation vector</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be translated</p></dd>
</dl></dd>
<dt><a name="40"><b class="cmd">::math::geometry::rotate</b> <i class="arg">angle</i> <i class="arg">polyline</i></a></dt>
<dd><p>Rotate a polyline over a given angle (degrees) around the origin</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">angle</i></dt>
<dd><p>Angle over which to rotate the polyline (degrees)</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be rotated</p></dd>
</dl></dd>
<dt><a name="41"><b class="cmd">::math::geometry::reflect</b> <i class="arg">angle</i> <i class="arg">polyline</i></a></dt>
<dd><p>Reflect a polyline in a line through the origin at a given angle (degrees) to the x-axis</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">angle</i></dt>
<dd><p>Angle of the line of reflection (degrees)</p></dd>
<dt>list <i class="arg">polyline</i></dt>
<dd><p>The polyline to be reflected</p></dd>
</dl></dd>
<dt><a name="42"><b class="cmd">::math::geometry::degToRad</b> <i class="arg">angle</i></a></dt>
<dd><p>Convert from degrees to radians</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">angle</i></dt>
<dd><p>Angle in degrees</p></dd>
</dl></dd>
<dt><a name="43"><b class="cmd">::math::geometry::radToDeg</b> <i class="arg">angle</i></a></dt>
<dd><p>Convert from radians to degrees</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">angle</i></dt>
<dd><p>Angle in radians</p></dd>
</dl></dd>
<dt><a name="44"><b class="cmd">::math::geometry::circle</b> <i class="arg">centre</i> <i class="arg">radius</i></a></dt>
<dd><p>Convenience procedure to create a circle from a point and a radius.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">centre</i></dt>
<dd><p>Coordinates of the circle centre</p></dd>
<dt>list <i class="arg">radius</i></dt>
<dd><p>Radius of the circle</p></dd>
</dl></dd>
<dt><a name="45"><b class="cmd">::math::geometry::circleTwoPoints</b> <i class="arg">point1</i> <i class="arg">point2</i></a></dt>
<dd><p>Convenience procedure to create a circle from two points on its circumference
The centre is the point between the two given points, the radius is half the
distance between them.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">point1</i></dt>
<dd><p>First point</p></dd>
<dt>list <i class="arg">point2</i></dt>
<dd><p>Second point</p></dd>
</dl></dd>
<dt><a name="46"><b class="cmd">::math::geometry::pointInsideCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></dt>
<dd><p>Determine if the given point is inside the circle or on the circumference (1)
or outside (0).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">point</i></dt>
<dd><p>Point to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not contain the point</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::geometry::lineIntersectsCircle</b> <i class="arg">line</i> <i class="arg">circle</i></a></dt>
<dd><p>Determine if the given line intersects the circle or touches it (1)
or does not (0).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">line</i></dt>
<dd><p>Line to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not be intersected</p></dd>
</dl></dd>
<dt><a name="48"><b class="cmd">::math::geometry::lineSegmentIntersectsCircle</b> <i class="arg">segment</i> <i class="arg">circle</i></a></dt>
<dd><p>Determine if the given line segment intersects the circle or touches it (1)
or does not (0).</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">segment</i></dt>
<dd><p>Line segment to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not be intersected</p></dd>
</dl></dd>
<dt><a name="49"><b class="cmd">::math::geometry::intersectionLineWithCircle</b> <i class="arg">line</i> <i class="arg">circle</i></a></dt>
<dd><p>Determine the points at which the given line intersects the circle. There can
be zero, one or two points. (If the line touches the circle or is close to it,
then one point is returned. An arbitrary margin of 1.0e-10 times the radius
is used to determine this situation.)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">line</i></dt>
<dd><p>Line to be checked</p></dd>
<dt>list <i class="arg">circle</i></dt>
<dd><p>Circle that may or may not be intersected</p></dd>
</dl></dd>
<dt><a name="50"><b class="cmd">::math::geometry::intersectionCircleWithCircle</b> <i class="arg">circle1</i> <i class="arg">circle2</i></a></dt>
<dd><p>Determine the points at which the given two circles intersect. There can
be zero, one or two points. (If the two circles touch the circle or are very close,
then one point is returned. An arbitrary margin of 1.0e-10 times the mean of the radii of
the two circles is used to determine this situation.)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">circle1</i></dt>
<dd><p>First circle</p></dd>
<dt>list <i class="arg">circle2</i></dt>
<dd><p>Second circle</p></dd>
</dl></dd>
<dt><a name="51"><b class="cmd">::math::geometry::tangentLinesToCircle</b> <i class="arg">point</i> <i class="arg">circle</i></a></dt>
<dd><p>Determine the tangent lines from the given point to the circle. There can
be zero, one or two lines. (If the point is on the cirucmference or very close to
the circle, then one line is returned. An arbitrary margin of 1.0e-10 times the
radius of the circle is used to determine this situation.)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">point</i></dt>
<dd><p>Point in question</p></dd>

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 ] <hr>
<div class="doctools">
<h1 class="doctools_title">math::special(n) 0.4 tcllib &quot;Tcl Math Library&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>math::special - Special mathematical functions</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl <span class="opt">?8.5?</span></b></li>
<li>package require <b class="pkgname">math::special <span class="opt">?0.4?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::math::special::Beta</b> <i class="arg">x</i> <i class="arg">y</i></a></li>
<li><a href="#2"><b class="cmd">::math::special::incBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i></a></li>
<li><a href="#3"><b class="cmd">::math::special::regIncBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i></a></li>
<li><a href="#4"><b class="cmd">::math::special::Gamma</b> <i class="arg">x</i></a></li>
<li><a href="#5"><b class="cmd">::math::special::digamma</b> <i class="arg">x</i></a></li>
<li><a href="#6"><b class="cmd">::math::special::erf</b> <i class="arg">x</i></a></li>
<li><a href="#7"><b class="cmd">::math::special::erfc</b> <i class="arg">x</i></a></li>
<li><a href="#8"><b class="cmd">::math::special::invnorm</b> <i class="arg">p</i></a></li>
<li><a href="#9"><b class="cmd">::math::special::J0</b> <i class="arg">x</i></a></li>
<li><a href="#10"><b class="cmd">::math::special::J1</b> <i class="arg">x</i></a></li>
<li><a href="#11"><b class="cmd">::math::special::Jn</b> <i class="arg">n</i> <i class="arg">x</i></a></li>
<li><a href="#12"><b class="cmd">::math::special::J1/2</b> <i class="arg">x</i></a></li>
<li><a href="#13"><b class="cmd">::math::special::J-1/2</b> <i class="arg">x</i></a></li>
<li><a href="#14"><b class="cmd">::math::special::I_n</b> <i class="arg">x</i></a></li>
<li><a href="#15"><b class="cmd">::math::special::cn</b> <i class="arg">u</i> <i class="arg">k</i></a></li>
<li><a href="#16"><b class="cmd">::math::special::dn</b> <i class="arg">u</i> <i class="arg">k</i></a></li>
<li><a href="#17"><b class="cmd">::math::special::sn</b> <i class="arg">u</i> <i class="arg">k</i></a></li>
<li><a href="#18"><b class="cmd">::math::special::elliptic_K</b> <i class="arg">k</i></a></li>
<li><a href="#19"><b class="cmd">::math::special::elliptic_E</b> <i class="arg">k</i></a></li>
<li><a href="#20"><b class="cmd">::math::special::exponential_Ei</b> <i class="arg">x</i></a></li>
<li><a href="#21"><b class="cmd">::math::special::exponential_En</b> <i class="arg">n</i> <i class="arg">x</i></a></li>
<li><a href="#22"><b class="cmd">::math::special::exponential_li</b> <i class="arg">x</i></a></li>
<li><a href="#23"><b class="cmd">::math::special::exponential_Ci</b> <i class="arg">x</i></a></li>
<li><a href="#24"><b class="cmd">::math::special::exponential_Si</b> <i class="arg">x</i></a></li>
<li><a href="#25"><b class="cmd">::math::special::exponential_Chi</b> <i class="arg">x</i></a></li>
<li><a href="#26"><b class="cmd">::math::special::exponential_Shi</b> <i class="arg">x</i></a></li>
<li><a href="#27"><b class="cmd">::math::special::fresnel_C</b> <i class="arg">x</i></a></li>
<li><a href="#28"><b class="cmd">::math::special::fresnel_S</b> <i class="arg">x</i></a></li>
<li><a href="#29"><b class="cmd">::math::special::sinc</b> <i class="arg">x</i></a></li>
<li><a href="#30"><b class="cmd">::math::special::legendre</b> <i class="arg">n</i></a></li>
<li><a href="#31"><b class="cmd">::math::special::chebyshev</b> <i class="arg">n</i></a></li>
<li><a href="#32"><b class="cmd">::math::special::laguerre</b> <i class="arg">alpha</i> <i class="arg">n</i></a></li>
<li><a href="#33"><b class="cmd">::math::special::hermite</b> <i class="arg">n</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>This package implements several so-called special functions, like
the Gamma function, the Bessel functions and such.</p>
<p>Each function is implemented by a procedure that bears its name (well,

             |             |             |             |
Fresnel      | C           |  all of R   |     --      |   < 2.0e-3
integrals    | S           |  all of R   |     --      |   < 2.0e-3
             |             |             |             |
general      | Beta        | (see Gamma) |     --      |   < 1.0e-9
             | Gamma       |  x != 0,-1, |     --      |   < 1.0e-9
             |             |  -2, ...    |             |
             | incBeta     |             |  a, b > 0   |   < 1.0e-9
             | regIncBeta  |             |  a, b > 0   |   < 1.0e-9
             | digamma     |  x != 0,-1  |             |   < 1.0e-9
             |             |  -2, ...    |             |
             |             |             |             |
             | sinc        |  all of R   |     --      |   exact
             |             |             |             |
orthogonal   | Legendre    |  all of R   | n = 0,1,... |   exact
polynomials  | Chebyshev   |  all of R   | n = 0,1,... |   exact
             | Laguerre    |  all of R   | n = 0,1,... |   exact
             |             |             | alpha el. R |
             | Hermite     |  all of R   | n = 0,1,... |   exact
</pre>
<p><em>Note:</em> Some of the error bounds are estimated, as no
&quot;formal&quot; bounds were available with the implemented approximation
method, others hold for the auxiliary functions used for estimating
the primary functions.</p>
<p>The following well-known functions are currently missing from the package:</p>
<ul class="doctools_itemized">
<li><p>Bessel functions of the second kind (Y_n, K_n)</p></li>
<li><p>Bessel functions of arbitrary order (and hence the Airy functions)</p></li>
<li><p>Chebyshev polynomials of the second kind (U_n)</p></li>

<li><p>The incomplete gamma function</p></li>
</ul>
</div>
<div id="section3" class="doctools_section"><h2><a name="section3">PROCEDURES</a></h2>
<p>The package defines the following public procedures:</p>
<dl class="doctools_definitions">
<dt><a name="1"><b class="cmd">::math::special::Beta</b> <i class="arg">x</i> <i class="arg">y</i></a></dt>
<dd><p>Compute the Beta function for arguments &quot;x&quot; and &quot;y&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>First argument for the Beta function</p></dd>
<dt>float <i class="arg">y</i></dt>
<dd><p>Second argument for the Beta function</p></dd>
</dl></dd>
<dt><a name="2"><b class="cmd">::math::special::incBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i></a></dt>
<dd><p>Compute the incomplete Beta function for argument &quot;x&quot; with parameters &quot;a&quot; and &quot;b&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>First parameter for the incomplete Beta function, a &gt; 0</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>Second parameter for the incomplete Beta function, b &gt; 0</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the incomplete Beta function</p></dd>
</dl></dd>
<dt><a name="3"><b class="cmd">::math::special::regIncBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i></a></dt>
<dd><p>Compute the regularized incomplete Beta function for argument &quot;x&quot; with parameters &quot;a&quot; and &quot;b&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>First parameter for the incomplete Beta function, a &gt; 0</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>Second parameter for the incomplete Beta function, b &gt; 0</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the regularized incomplete Beta function</p></dd>
</dl></dd>
<dt><a name="4"><b class="cmd">::math::special::Gamma</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the Gamma function for argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Gamma function</p></dd>
</dl></dd>
<dt><a name="5"><b class="cmd">::math::special::digamma</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the digamma function (psi) for argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the digamma function</p></dd>
</dl></dd>
<dt><a name="6"><b class="cmd">::math::special::erf</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the error function for argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the error function</p></dd>
</dl></dd>
<dt><a name="7"><b class="cmd">::math::special::erfc</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the complementary error function for argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the complementary error function</p></dd>
</dl></dd>
<dt><a name="8"><b class="cmd">::math::special::invnorm</b> <i class="arg">p</i></a></dt>
<dd><p>Compute the inverse of the normal distribution function for argument &quot;p&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">p</i></dt>
<dd><p>Argument for the inverse normal distribution function
(p must be greater than 0 and lower than 1)</p></dd>
</dl></dd>
<dt><a name="9"><b class="cmd">::math::special::J0</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the zeroth-order Bessel function of the first kind for the
argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Bessel function</p></dd>
</dl></dd>
<dt><a name="10"><b class="cmd">::math::special::J1</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the first-order Bessel function of the first kind for the
argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Bessel function</p></dd>
</dl></dd>
<dt><a name="11"><b class="cmd">::math::special::Jn</b> <i class="arg">n</i> <i class="arg">x</i></a></dt>
<dd><p>Compute the nth-order Bessel function of the first kind for the
argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>integer <i class="arg">n</i></dt>
<dd><p>Order of the Bessel function</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Bessel function</p></dd>
</dl></dd>
<dt><a name="12"><b class="cmd">::math::special::J1/2</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the half-order Bessel function of the first kind for the
argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Bessel function</p></dd>
</dl></dd>
<dt><a name="13"><b class="cmd">::math::special::J-1/2</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the minus-half-order Bessel function of the first kind for the
argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the Bessel function</p></dd>
</dl></dd>
<dt><a name="14"><b class="cmd">::math::special::I_n</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the modified Bessel function of the first kind of order n for
the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">x</i></dt>
<dd><p>Positive integer order of the function</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="15"><b class="cmd">::math::special::cn</b> <i class="arg">u</i> <i class="arg">k</i></a></dt>
<dd><p>Compute the elliptic function <em>cn</em> for the argument &quot;u&quot; and
parameter &quot;k&quot;.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">u</i></dt>
<dd><p>Argument for the function</p></dd>
<dt>float <i class="arg">k</i></dt>
<dd><p>Parameter</p></dd>
</dl></dd>
<dt><a name="16"><b class="cmd">::math::special::dn</b> <i class="arg">u</i> <i class="arg">k</i></a></dt>
<dd><p>Compute the elliptic function <em>dn</em> for the argument &quot;u&quot; and
parameter &quot;k&quot;.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">u</i></dt>
<dd><p>Argument for the function</p></dd>
<dt>float <i class="arg">k</i></dt>
<dd><p>Parameter</p></dd>
</dl></dd>
<dt><a name="17"><b class="cmd">::math::special::sn</b> <i class="arg">u</i> <i class="arg">k</i></a></dt>
<dd><p>Compute the elliptic function <em>sn</em> for the argument &quot;u&quot; and
parameter &quot;k&quot;.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">u</i></dt>
<dd><p>Argument for the function</p></dd>
<dt>float <i class="arg">k</i></dt>
<dd><p>Parameter</p></dd>
</dl></dd>
<dt><a name="18"><b class="cmd">::math::special::elliptic_K</b> <i class="arg">k</i></a></dt>
<dd><p>Compute the complete elliptic integral of the first kind
for the argument &quot;k&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">k</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="19"><b class="cmd">::math::special::elliptic_E</b> <i class="arg">k</i></a></dt>
<dd><p>Compute the complete elliptic integral of the second kind
for the argument &quot;k&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">k</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="20"><b class="cmd">::math::special::exponential_Ei</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the exponential integral of the second kind
for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x != 0)</p></dd>
</dl></dd>
<dt><a name="21"><b class="cmd">::math::special::exponential_En</b> <i class="arg">n</i> <i class="arg">x</i></a></dt>
<dd><p>Compute the exponential integral of the first kind
for the argument &quot;x&quot; and order n</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">n</i></dt>
<dd><p>Order of the integral (n &gt;= 0)</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt;= 0)</p></dd>
</dl></dd>
<dt><a name="22"><b class="cmd">::math::special::exponential_li</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the logarithmic integral for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt; 0)</p></dd>
</dl></dd>
<dt><a name="23"><b class="cmd">::math::special::exponential_Ci</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the cosine integral for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt; 0)</p></dd>
</dl></dd>
<dt><a name="24"><b class="cmd">::math::special::exponential_Si</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the sine integral for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt; 0)</p></dd>
</dl></dd>
<dt><a name="25"><b class="cmd">::math::special::exponential_Chi</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the hyperbolic cosine integral for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt; 0)</p></dd>
</dl></dd>
<dt><a name="26"><b class="cmd">::math::special::exponential_Shi</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the hyperbolic sine integral for the argument &quot;x&quot;</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function (x &gt; 0)</p></dd>
</dl></dd>
<dt><a name="27"><b class="cmd">::math::special::fresnel_C</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the Fresnel cosine integral for real argument x</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="28"><b class="cmd">::math::special::fresnel_S</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the Fresnel sine integral for real argument x</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="29"><b class="cmd">::math::special::sinc</b> <i class="arg">x</i></a></dt>
<dd><p>Compute the sinc function for real argument x</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>Argument for the function</p></dd>
</dl></dd>
<dt><a name="30"><b class="cmd">::math::special::legendre</b> <i class="arg">n</i></a></dt>
<dd><p>Return the Legendre polynomial of degree n
(see <span class="sectref"><a href="#section4">THE ORTHOGONAL POLYNOMIALS</a></span>)</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">n</i></dt>
<dd><p>Degree of the polynomial</p></dd>
</dl></dd>
<dt><a name="31"><b class="cmd">::math::special::chebyshev</b> <i class="arg">n</i></a></dt>
<dd><p>Return the Chebyshev polynomial of degree n (of the first kind)</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">n</i></dt>
<dd><p>Degree of the polynomial</p></dd>
</dl></dd>
<dt><a name="32"><b class="cmd">::math::special::laguerre</b> <i class="arg">alpha</i> <i class="arg">n</i></a></dt>
<dd><p>Return the Laguerre polynomial of degree n with parameter alpha</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>Parameter of the Laguerre polynomial</p></dd>
<dt>int <i class="arg">n</i></dt>
<dd><p>Degree of the polynomial</p></dd>
</dl></dd>
<dt><a name="33"><b class="cmd">::math::special::hermite</b> <i class="arg">n</i></a></dt>
<dd><p>Return the Hermite polynomial of degree n</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">n</i></dt>
<dd><p>Degree of the polynomial</p></dd>
</dl></dd>
</dl>
</div>

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<li><a href="#87"><b class="cmd">::math::statistics::cdf-laplace</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></li>
<li><a href="#88"><b class="cmd">::math::statistics::cdf-kumaraswamy</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></li>
<li><a href="#89"><b class="cmd">::math::statistics::cdf-negative-binomial</b> <i class="arg">r</i> <i class="arg">p</i> <i class="arg">value</i></a></li>
<li><a href="#90"><b class="cmd">::math::statistics::empirical-distribution</b> <i class="arg">values</i></a></li>
<li><a href="#91"><b class="cmd">::math::statistics::random-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#92"><b class="cmd">::math::statistics::random-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></li>
<li><a href="#93"><b class="cmd">::math::statistics::random-exponential</b> <i class="arg">mean</i> <i class="arg">number</i></a></li>
<li><a href="#94"><b class="cmd">::math::statistics::random-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></li>
<li><a href="#95"><b class="cmd">::math::statistics::random-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></li>
<li><a href="#96"><b class="cmd">::math::statistics::random-symmetric-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></li>
<li><a href="#97"><b class="cmd">::math::statistics::random-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">number</i></a></li>
<li><a href="#98"><b class="cmd">::math::statistics::random-poisson</b> <i class="arg">mu</i> <i class="arg">number</i></a></li>
<li><a href="#99"><b class="cmd">::math::statistics::random-chisquare</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#100"><b class="cmd">::math::statistics::random-student-t</b> <i class="arg">df</i> <i class="arg">number</i></a></li>
<li><a href="#101"><b class="cmd">::math::statistics::random-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></li>
<li><a href="#102"><b class="cmd">::math::statistics::random-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#103"><b class="cmd">::math::statistics::random-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#104"><b class="cmd">::math::statistics::random-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></li>
<li><a href="#105"><b class="cmd">::math::statistics::random-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#106"><b class="cmd">::math::statistics::random-laplace</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></li>
<li><a href="#107"><b class="cmd">::math::statistics::random-kumaraswamy</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></li>
<li><a href="#108"><b class="cmd">::math::statistics::random-negative-binomial</b> <i class="arg">r</i> <i class="arg">p</i> <i class="arg">number</i></a></li>
<li><a href="#109"><b class="cmd">::math::statistics::histogram-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">limits</i> <i class="arg">number</i></a></li>
<li><a href="#110"><b class="cmd">::math::statistics::incompleteGamma</b> <i class="arg">x</i> <i class="arg">p</i> <span class="opt">?tol?</span></a></li>
<li><a href="#111"><b class="cmd">::math::statistics::incompleteBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i> <span class="opt">?tol?</span></a></li>
<li><a href="#112"><b class="cmd">::math::statistics::estimate-pareto</b> <i class="arg">values</i></a></li>
<li><a href="#113"><b class="cmd">::math::statistics::estimate-exponential</b> <i class="arg">values</i></a></li>
<li><a href="#114"><b class="cmd">::math::statistics::estimate-laplace</b> <i class="arg">values</i></a></li>
<li><a href="#115"><b class="cmd">::math::statistics::estimante-negative-binomial</b> <i class="arg">r</i> <i class="arg">values</i></a></li>
<li><a href="#116"><b class="cmd">::math::statistics::filter</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#117"><b class="cmd">::math::statistics::map</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></li>
<li><a href="#118"><b class="cmd">::math::statistics::samplescount</b> <i class="arg">varname</i> <i class="arg">list</i> <i class="arg">expression</i></a></li>
<li><a href="#119"><b class="cmd">::math::statistics::subdivide</b></a></li>
<li><a href="#120"><b class="cmd">::math::statistics::plot-scale</b> <i class="arg">canvas</i> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">ymin</i> <i class="arg">ymax</i></a></li>
<li><a href="#121"><b class="cmd">::math::statistics::plot-xydata</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#122"><b class="cmd">::math::statistics::plot-xyline</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></li>
<li><a href="#123"><b class="cmd">::math::statistics::plot-tdata</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#124"><b class="cmd">::math::statistics::plot-tline</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></li>
<li><a href="#125"><b class="cmd">::math::statistics::plot-histogram</b> <i class="arg">canvas</i> <i class="arg">counts</i> <i class="arg">limits</i> <i class="arg">tag</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">math::statistics</b> package contains functions and procedures for
basic statistical data analysis, such as:</p>
<ul class="doctools_itemized">

Returns the Kruskal-Wallis statistic and the probability that that
value would occur assuming the medians of the populations are
equal.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">args</i></dt>
<dd><p>- Two or more lists of data</p></dd>
</dl></dd>
<dt><a name="38"><b class="cmd">::math::statistics::test-Levene</b> <i class="arg">groups</i></a></dt>
<dd><p>Compute the Levene statistic to determine if groups of data have the
same variance (are homoscadastic) or not. The data are organised
in groups. This version uses the mean of the data as the measure
to determine the deviations. The statistic is equivalent to an
F statistic with degrees of freedom k-1 and N-k, k being the
number of groups and N the total number of data.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">groups</i></dt>
<dd><p>- List of groups of data</p></dd>
</dl></dd>
<dt><a name="39"><b class="cmd">::math::statistics::test-Brown-Forsythe</b> <i class="arg">groups</i></a></dt>
<dd><p>Compute the Brown-Forsythe statistic to determine if groups of data have the
same variance (are homoscadastic) or not. Like the Levene test, but this
version uses the median of the data.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">groups</i></dt>
<dd><p>- List of groups of data</p></dd>
</dl></dd>
<dt><a name="40"><b class="cmd">::math::statistics::group-rank</b> <i class="arg">args</i></a></dt>
<dd><p>Rank the groups of data with respect to the complete set.
Returns a list consisting of the group ID, the value and the rank
(possibly a rational number, in case of ties) for each data item.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">args</i></dt>
<dd><p>- Two or more lists of data</p></dd>
</dl></dd>
<dt><a name="41"><b class="cmd">::math::statistics::test-Wilcoxon</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></dt>
<dd><p>Compute the Wilcoxon test statistic to determine if two samples have the
same median or not. (The statistic can be regarded as standard normal, if the
sample sizes are both larger than 10.) Returns the value of this statistic.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">sample_a</i></dt>
<dd><p>- List of data comprising the first sample</p></dd>
<dt>list <i class="arg">sample_b</i></dt>
<dd><p>- List of data comprising the second sample</p></dd>
</dl></dd>
<dt><a name="42"><b class="cmd">::math::statistics::spearman-rank</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></dt>
<dd><p>Return the Spearman rank correlation as an alternative to the ordinary (Pearson's) correlation
coefficient. The two samples should have the same number of data.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">sample_a</i></dt>
<dd><p>- First list of data</p></dd>
<dt>list <i class="arg">sample_b</i></dt>
<dd><p>- Second list of data</p></dd>
</dl></dd>
<dt><a name="43"><b class="cmd">::math::statistics::spearman-rank-extended</b> <i class="arg">sample_a</i> <i class="arg">sample_b</i></a></dt>
<dd><p>Return the Spearman rank correlation as an alternative to the ordinary (Pearson's) correlation
coefficient as well as additional data. The two samples should have the same number of data.
The procedure returns the correlation coefficient, the number of data pairs used and the
z-score, an approximately standard normal statistic, indicating the significance of the correlation.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">sample_a</i></dt>
<dd><p>- First list of data</p></dd>
<dt>list <i class="arg">sample_b</i></dt>
<dd><p>- Second list of data</p></dd>
</dl></dd>
<dt><a name="44"><b class="cmd">::math::statistics::kernel-density</b> <i class="arg">data</i> opt <i class="arg">-option value</i> ...</a></dt>
<dd><p>Return the density function based on kernel density estimation. The procedure is controlled by
a small set of options, each of which is given a reasonable default.</p>
<p>The return value consists of three lists: the centres of the bins, the associated probability
density and a list of computational parameters (begin and end of the interval, mean and standard
deviation and the used bandwidth). The computational parameters can be used for further analysis.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">data</i></dt>

<dd><p>Begin and end of the interval for
which the density is returned (default: mean +/- 3*standard deviation)</p></dd>
<dt><b class="option">-kernel</b> <i class="arg">function</i></dt>
<dd><p>Kernel to be used (One of: gaussian, cosine,
epanechnikov, uniform, triangular, biweight, logistic; default: gaussian)</p></dd>
</dl></dd>
</dl></dd>
<dt><a name="45"><b class="cmd">::math::statistics::bootstrap</b> <i class="arg">data</i> <i class="arg">sampleSize</i> <span class="opt">?numberSamples?</span></a></dt>
<dd><p>Create a subsample or subsamples from a given list of data. The data in the samples are chosen
from this list - multiples may occur. If there is only one subsample, the sample itself
is returned (as a list of &quot;sampleSize&quot; values), otherwise a list of samples is returned.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">data</i></dt>
<dd><p>List of values to chose from</p></dd>
<dt>int <i class="arg">sampleSize</i></dt>
<dd><p>Number of values per sample</p></dd>
<dt>int <i class="arg">numberSamples</i></dt>
<dd><p>Number of samples (default: 1)</p></dd>
</dl></dd>
<dt><a name="46"><b class="cmd">::math::statistics::wasserstein-distance</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Wasserstein distance or earth mover's distance for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="47"><b class="cmd">::math::statistics::kl-divergence</b> <i class="arg">prob1</i> <i class="arg">prob2</i></a></dt>
<dd><p>Compute the Kullback-Leibler (KL) divergence for two equidstantly spaced histograms
or probability densities. The histograms need not to be normalised to sum to one,
but they must have the same number of entries.</p>
<p>Note: the histograms are assumed to be based on the same equidistant intervals.
As the bounds are not passed, the value is expressed in the length of the intervals.</p>
<p>Note also that the KL divergence is not symmetric and that the second histogram
should not contain zeroes in places where the first histogram has non-zero values.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">prob1</i></dt>
<dd><p>List of values for the first histogram/probability density</p></dd>
<dt>list <i class="arg">prob2</i></dt>
<dd><p>List of values for the second histogram/probability density</p></dd>
</dl></dd>
<dt><a name="48"><b class="cmd">::math::statistics::logistic-model</b> <i class="arg">xdata</i> <i class="arg">ydata</i></a></dt>
<dd><p>Estimate the coefficients of the logistic model that fits the data best. The data consist
of independent x-values and the outcome 0 or 1 for each of the x-values. The result
can be used to estimate the probability that a certain x-value gives 1.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">xdata</i></dt>
<dd><p>List of values for which the success (1) or failure (0) is known</p></dd>
<dt>list <i class="arg">ydata</i></dt>
<dd><p>List of successes or failures corresponding to each value in <i class="term">xdata</i>.</p></dd>
</dl></dd>
<dt><a name="49"><b class="cmd">::math::statistics::logistic-probability</b> <i class="arg">coeffs</i> <i class="arg">x</i></a></dt>
<dd><p>Calculate the probability of success for the value <i class="term">x</i> given the coefficients of the
logistic model.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">coeffs</i></dt>
<dd><p>List of coefficients as determine by the <b class="cmd">logistic-model</b> command</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>X-value for which the probability needs to be determined</p></dd>

<p>In addition to these two, it provides a procedure (tstat)
for calculating the value of the t-statistic for the specified number of
degrees of freedom that is required to demonstrate a given level of
significance.</p>
<p>Note: These procedures depend on the math::linearalgebra package.</p>
<p><em>Description of the procedures</em></p>
<dl class="doctools_definitions">
<dt><a name="50"><b class="cmd">::math::statistics::tstat</b> <i class="arg">dof</i> <span class="opt">?alpha?</span></a></dt>
<dd><p>Returns the value of the t-distribution t* satisfying</p>
<pre class="doctools_example">
    P(t*)  =  1 - alpha/2
    P(-t*) =  alpha/2
</pre>
<p>for the number of degrees of freedom dof.</p>
<p>Given a sample of normally-distributed data x, with an

the given confidence level.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">dof</i></dt>
<dd><p>Number of degrees of freedom</p></dd>
<dt>float <i class="arg">alpha</i></dt>
<dd><p>Confidence level of the t-distribution. Defaults to 0.05.</p></dd>
</dl></dd>
<dt><a name="51"><b class="cmd">::math::statistics::mv-wls</b> <i class="arg">wt1</i> <i class="arg">weights_and_values</i></a></dt>
<dd><p>Carries out a weighted least squares linear regression for
the data points provided, with weights assigned to each point.</p>
<p>The linear model is of the form</p>
<pre class="doctools_example">
    y = b0 + b1 * x1 + b2 * x2 ... + bN * xN + error
</pre>
<p>and each point satisfies</p>

<dt>list <i class="arg">weights_and_values</i></dt>
<dd><p>A list consisting of: the weight for the first observation, the data
for the first observation (as a sublist), the weight for the second
observation (as a sublist) and so on. The sublists of data are organised
as lists of the value of the dependent variable y and the independent
variables x1, x2 to xN.</p></dd>
</dl></dd>
<dt><a name="52"><b class="cmd">::math::statistics::mv-ols</b> <i class="arg">values</i></a></dt>
<dd><p>Carries out an ordinary least squares linear regression for
the data points provided.</p>
<p>This procedure simply calls ::mvlinreg::wls with the weights
set to 1.0, and returns the same information.</p></dd>
</dl>
<p><em>Example of the use:</em></p>
<pre class="doctools_example">

<li><p>The cumulative density (cdf-*)</p></li>
<li><p>Quantiles for the given distribution (quantiles-*)</p></li>
<li><p>Histograms for the given distribution (histogram-*)</p></li>
<li><p>List of random values with the given distribution (random-*)</p></li>
</ul>
<p>The following procedures have been implemented:</p>
<dl class="doctools_definitions">
<dt><a name="53"><b class="cmd">::math::statistics::pdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a normal distribution with
given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="54"><b class="cmd">::math::statistics::pdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a log-normal distribution with
given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="55"><b class="cmd">::math::statistics::pdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="56"><b class="cmd">::math::statistics::pdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="57"><b class="cmd">::math::statistics::pdf-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a triangular
distribution with given extremes. If the argument min is lower than the argument max, then smaller
values have higher probability and vice versa. In the first case the probability
density function is of the form <em>f(x) = 2(1-x)</em> and the other case it is of the form <em>f(x) = 2x</em>.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="58"><b class="cmd">::math::statistics::pdf-symmetric-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a symmetric triangular
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="59"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gamma
distribution with given shape and rate parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="60"><b class="cmd">::math::statistics::pdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></dt>
<dd><p>Return the probability of a given number of occurrences in the same
interval (k) for a Poisson distribution with given mean (mu)</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean number of occurrences</p></dd>
<dt>int <i class="arg">k</i></dt>
<dd><p>- Number of occurences</p></dd>
</dl></dd>
<dt><a name="61"><b class="cmd">::math::statistics::pdf-chisquare</b> <i class="arg">df</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a chi square
distribution with given degrees of freedom</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="62"><b class="cmd">::math::statistics::pdf-student-t</b> <i class="arg">df</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Student's t
distribution with given degrees of freedom</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="63"><b class="cmd">::math::statistics::pdf-gamma</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gamma
distribution with given shape and rate parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="64"><b class="cmd">::math::statistics::pdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Beta
distribution with given shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="65"><b class="cmd">::math::statistics::pdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Weibull
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="66"><b class="cmd">::math::statistics::pdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Gumbel
distribution with given location and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="67"><b class="cmd">::math::statistics::pdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Pareto
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="68"><b class="cmd">::math::statistics::pdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Cauchy
distribution with given location and shape parameters. Note that the Cauchy distribution
has no finite higher-order moments.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="69"><b class="cmd">::math::statistics::pdf-laplace</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Laplace
distribution with given location and shape parameters. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter (mean)</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="70"><b class="cmd">::math::statistics::pdf-kumaraswamy</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a Kumaraswamy
distribution with given parameters a and b. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- Parameter a</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Parameter b</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="71"><b class="cmd">::math::statistics::pdf-negative-binomial</b> <i class="arg">r</i> <i class="arg">p</i> <i class="arg">value</i></a></dt>
<dd><p>Return the probability of a given value for a negative binomial
distribution with an allowed number of failures and the probability of success.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">r</i></dt>
<dd><p>- Allowed number of failures (at least 1)</p></dd>
<dt>float <i class="arg">p</i></dt>
<dd><p>- Probability of success</p></dd>
<dt>int <i class="arg">value</i></dt>
<dd><p>- Number of successes for which the probability is to be returned</p></dd>
</dl></dd>
<dt><a name="72"><b class="cmd">::math::statistics::cdf-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a normal
distribution with given mean and standard deviation, that is the
probability for values up to the given one.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="73"><b class="cmd">::math::statistics::cdf-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a log-normal
distribution with given mean and standard deviation, that is the
probability for values up to the given one.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="74"><b class="cmd">::math::statistics::cdf-exponential</b> <i class="arg">mean</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="75"><b class="cmd">::math::statistics::cdf-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="76"><b class="cmd">::math::statistics::cdf-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a triangular
distribution with given extremes. If xmin &lt; xmax, then lower values have
a higher probability and vice versa, see also <em>pdf-triangular</em></p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="77"><b class="cmd">::math::statistics::cdf-symmetric-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a symmetric triangular
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="78"><b class="cmd">::math::statistics::cdf-students-t</b> <i class="arg">degrees</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Student's t
distribution with given number of degrees.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">degrees</i></dt>
<dd><p>- Number of degrees of freedom</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="79"><b class="cmd">::math::statistics::cdf-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Gamma
distribution with given shape and rate parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the cumulative probability is required</p></dd>
</dl></dd>
<dt><a name="80"><b class="cmd">::math::statistics::cdf-poisson</b> <i class="arg">mu</i> <i class="arg">k</i></a></dt>
<dd><p>Return the cumulative probability of a given number of occurrences in
the same interval (k) for a Poisson distribution with given mean (mu).</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean number of occurrences</p></dd>
<dt>int <i class="arg">k</i></dt>
<dd><p>- Number of occurences</p></dd>
</dl></dd>
<dt><a name="81"><b class="cmd">::math::statistics::cdf-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Beta
distribution with given shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="82"><b class="cmd">::math::statistics::cdf-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Weibull
distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="83"><b class="cmd">::math::statistics::cdf-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Gumbel
distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="84"><b class="cmd">::math::statistics::cdf-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Pareto
distribution with given scale and shape parameters</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="85"><b class="cmd">::math::statistics::cdf-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Cauchy
distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="86"><b class="cmd">::math::statistics::cdf-F</b> <i class="arg">nf1</i> <i class="arg">nf2</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for an F
distribution with nf1 and nf2 degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">nf1</i></dt>
<dd><p>- Degrees of freedom for the numerator</p></dd>
<dt>float <i class="arg">nf2</i></dt>
<dd><p>- Degrees of freedom for the denominator</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="87"><b class="cmd">::math::statistics::cdf-laplace</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Laplace
distribution with given location and shape parameters. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter (mean)</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="88"><b class="cmd">::math::statistics::cdf-kumaraswamy</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a Kumaraswamy
distribution with given parameters a and b. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- Parameter a</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Parameter b</p></dd>
<dt>float <i class="arg">value</i></dt>
<dd><p>- Value for which the probability is required</p></dd>
</dl></dd>
<dt><a name="89"><b class="cmd">::math::statistics::cdf-negative-binomial</b> <i class="arg">r</i> <i class="arg">p</i> <i class="arg">value</i></a></dt>
<dd><p>Return the cumulative probability of a given value for a negative binomial
distribution with an allowed number of failures and the probability of success.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">r</i></dt>
<dd><p>- Allowed number of failures (at least 1)</p></dd>
<dt>float <i class="arg">p</i></dt>
<dd><p>- Probability of success</p></dd>
<dt>int <i class="arg">value</i></dt>
<dd><p>- Greatest number of successes</p></dd>
</dl></dd>
<dt><a name="90"><b class="cmd">::math::statistics::empirical-distribution</b> <i class="arg">values</i></a></dt>
<dd><p>Return a list of values and their empirical probability. The values are sorted in increasing order.
(The implementation follows the description at the corresponding Wikipedia page)</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of data to be examined</p></dd>
</dl></dd>
<dt><a name="91"><b class="cmd">::math::statistics::random-normal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a normal
distribution with given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="92"><b class="cmd">::math::statistics::random-lognormal</b> <i class="arg">mean</i> <i class="arg">stdev</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a log-normal
distribution with given mean and standard deviation.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>float <i class="arg">stdev</i></dt>
<dd><p>- Standard deviation of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="93"><b class="cmd">::math::statistics::random-exponential</b> <i class="arg">mean</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying an exponential
distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mean</i></dt>
<dd><p>- Mean value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="94"><b class="cmd">::math::statistics::random-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a uniform
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="95"><b class="cmd">::math::statistics::random-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a triangular
distribution with given extremes. If xmin &lt; xmax, then lower values have a higher probability
and vice versa (see also <em>pdf-triangular</em>.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="96"><b class="cmd">::math::statistics::random-symmetric-triangular</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a symmetric triangular
distribution with given extremes.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="97"><b class="cmd">::math::statistics::random-gamma</b> <i class="arg">alpha</i> <i class="arg">beta</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Gamma distribution with given shape and rate parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">alpha</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>float <i class="arg">beta</i></dt>
<dd><p>- Rate parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="98"><b class="cmd">::math::statistics::random-poisson</b> <i class="arg">mu</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Poisson distribution with given mean.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">mu</i></dt>
<dd><p>- Mean of the distribution</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="99"><b class="cmd">::math::statistics::random-chisquare</b> <i class="arg">df</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a chi square distribution with given degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="100"><b class="cmd">::math::statistics::random-student-t</b> <i class="arg">df</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Student's t distribution with given degrees of freedom.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">df</i></dt>
<dd><p>- Degrees of freedom</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="101"><b class="cmd">::math::statistics::random-beta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Beta distribution with given shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="102"><b class="cmd">::math::statistics::random-weibull</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Weibull distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="103"><b class="cmd">::math::statistics::random-gumbel</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Gumbel distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="104"><b class="cmd">::math::statistics::random-pareto</b> <i class="arg">scale</i> <i class="arg">shape</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Pareto distribution with given scale and shape parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>float <i class="arg">shape</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="105"><b class="cmd">::math::statistics::random-cauchy</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying
a Cauchy distribution with given location and scale parameters.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Scale parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="106"><b class="cmd">::math::statistics::random-laplace</b> <i class="arg">location</i> <i class="arg">scale</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisfying a Laplace
distribution with given location and shape parameters. The Laplace distribution
consists of two exponential functions, is peaked and has heavier tails than the
normal distribution.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">location</i></dt>
<dd><p>- Location parameter (mean)</p></dd>
<dt>float <i class="arg">scale</i></dt>
<dd><p>- Shape parameter</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="107"><b class="cmd">::math::statistics::random-kumaraswamy</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisying a Kumaraswamy
distribution with given parameters a and b. The Kumaraswamy distribution
is related to the Beta distribution, but has a tractable cumulative distribution function.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- Parameter a</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Parameter b</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="108"><b class="cmd">::math::statistics::random-negative-binomial</b> <i class="arg">r</i> <i class="arg">p</i> <i class="arg">number</i></a></dt>
<dd><p>Return a list of &quot;number&quot; random values satisying a negative binomial distribution.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">r</i></dt>
<dd><p>- Allowed number of failures (at least 1)</p></dd>
<dt>float <i class="arg">p</i></dt>
<dd><p>- Probability of success</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Number of values to be returned</p></dd>
</dl></dd>
<dt><a name="109"><b class="cmd">::math::statistics::histogram-uniform</b> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">limits</i> <i class="arg">number</i></a></dt>
<dd><p>Return the expected histogram for a uniform distribution.</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum value of the distribution</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum value of the distribution</p></dd>
<dt>list <i class="arg">limits</i></dt>
<dd><p>- Upper limits for the buckets in the histogram</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- Total number of &quot;observations&quot; in the histogram</p></dd>
</dl></dd>
<dt><a name="110"><b class="cmd">::math::statistics::incompleteGamma</b> <i class="arg">x</i> <i class="arg">p</i> <span class="opt">?tol?</span></a></dt>
<dd><p>Evaluate the incomplete Gamma integral</p>
<pre class="doctools_example">
                    1       / x               p-1
      P(p,x) =  --------   |   dt exp(-t) * t
                Gamma(p)  / 0
</pre>
<dl class="doctools_arguments">
<dt>float <i class="arg">x</i></dt>
<dd><p>- Value of x (limit of the integral)</p></dd>
<dt>float <i class="arg">p</i></dt>
<dd><p>- Value of p in the integrand</p></dd>
<dt>float <i class="arg">tol</i></dt>
<dd><p>- Required tolerance (default: 1.0e-9)</p></dd>
</dl></dd>
<dt><a name="111"><b class="cmd">::math::statistics::incompleteBeta</b> <i class="arg">a</i> <i class="arg">b</i> <i class="arg">x</i> <span class="opt">?tol?</span></a></dt>
<dd><p>Evaluate the incomplete Beta integral</p>
<dl class="doctools_arguments">
<dt>float <i class="arg">a</i></dt>
<dd><p>- First shape parameter</p></dd>
<dt>float <i class="arg">b</i></dt>
<dd><p>- Second shape parameter</p></dd>
<dt>float <i class="arg">x</i></dt>
<dd><p>- Value of x (limit of the integral)</p></dd>
<dt>float <i class="arg">tol</i></dt>
<dd><p>- Required tolerance (default: 1.0e-9)</p></dd>
</dl></dd>
<dt><a name="112"><b class="cmd">::math::statistics::estimate-pareto</b> <i class="arg">values</i></a></dt>
<dd><p>Estimate the parameters for the Pareto distribution that comes closest to the given values.
Returns the estimated scale and shape parameters, as well as the standard error for the shape parameter.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of values, assumed to be distributed according to a Pareto distribution</p></dd>
</dl></dd>
<dt><a name="113"><b class="cmd">::math::statistics::estimate-exponential</b> <i class="arg">values</i></a></dt>
<dd><p>Estimate the parameter for the exponential distribution that comes closest to the given values.
Returns an estimate of the one parameter and of the standard error.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of values, assumed to be distributed according to an exponential distribution</p></dd>
</dl></dd>
<dt><a name="114"><b class="cmd">::math::statistics::estimate-laplace</b> <i class="arg">values</i></a></dt>
<dd><p>Estimate the parameters for the Laplace distribution that comes closest to the given values.
Returns an estimate of respectively the location and scale parameters, based on maximum likelihood.</p>
<dl class="doctools_arguments">
<dt>list <i class="arg">values</i></dt>
<dd><p>- List of values, assumed to be distributed according to an exponential distribution</p></dd>
</dl></dd>
<dt><a name="115"><b class="cmd">::math::statistics::estimante-negative-binomial</b> <i class="arg">r</i> <i class="arg">values</i></a></dt>
<dd><p>Estimate the probability of success for the negative binomial distribution that comes closest to the given values.
The allowed number of failures must be given.</p>
<dl class="doctools_arguments">
<dt>int <i class="arg">r</i></dt>
<dd><p>- Allowed number of failures (at least 1)</p></dd>
<dt>int <i class="arg">number</i></dt>
<dd><p>- List of values, assumed to be distributed according to a negative binomial distribution.</p></dd>
</dl></dd>
</dl>
<p>TO DO: more function descriptions to be added</p>
</div>
<div id="section5" class="doctools_section"><h2><a name="section5">DATA MANIPULATION</a></h2>
<p>The data manipulation procedures act on lists or lists of lists:</p>
<dl class="doctools_definitions">
<dt><a name="116"><b class="cmd">::math::statistics::filter</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the data for which the logical
expression is true (this command works analogously to the command <b class="cmd"><a href="../../../../index.html#foreach">foreach</a></b>).</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Logical expression using the variable name</p></dd>
</dl></dd>
<dt><a name="117"><b class="cmd">::math::statistics::map</b> <i class="arg">varname</i> <i class="arg">data</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the data that are transformed via the
expression.</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Expression to be used to transform (map) the data</p></dd>
</dl></dd>
<dt><a name="118"><b class="cmd">::math::statistics::samplescount</b> <i class="arg">varname</i> <i class="arg">list</i> <i class="arg">expression</i></a></dt>
<dd><p>Return a list consisting of the <i class="term">counts</i> of all data in the
sublists of the &quot;list&quot; argument for which the expression is true.</p>
<dl class="doctools_arguments">
<dt>string <i class="arg">varname</i></dt>
<dd><p>- Name of the variable used in the expression</p></dd>
<dt>list <i class="arg">data</i></dt>
<dd><p>- List of sublists, each containing the data</p></dd>
<dt>string <i class="arg">expression</i></dt>
<dd><p>- Logical expression to test the data (defaults to
&quot;true&quot;).</p></dd>
</dl></dd>
<dt><a name="119"><b class="cmd">::math::statistics::subdivide</b></a></dt>
<dd><p>Routine <em>PM</em> - not implemented yet</p></dd>
</dl>
</div>
<div id="section6" class="doctools_section"><h2><a name="section6">PLOT PROCEDURES</a></h2>
<p>The following simple plotting procedures are available:</p>
<dl class="doctools_definitions">
<dt><a name="120"><b class="cmd">::math::statistics::plot-scale</b> <i class="arg">canvas</i> <i class="arg">xmin</i> <i class="arg">xmax</i> <i class="arg">ymin</i> <i class="arg">ymax</i></a></dt>
<dd><p>Set the scale for a plot in the given canvas. All plot routines expect
this function to be called first. There is no automatic scaling
provided.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>float <i class="arg">xmin</i></dt>
<dd><p>- Minimum x value</p></dd>
<dt>float <i class="arg">xmax</i></dt>
<dd><p>- Maximum x value</p></dd>
<dt>float <i class="arg">ymin</i></dt>
<dd><p>- Minimum y value</p></dd>
<dt>float <i class="arg">ymax</i></dt>
<dd><p>- Maximum y value</p></dd>
</dl></dd>
<dt><a name="121"><b class="cmd">::math::statistics::plot-xydata</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a collection of dots. The tag can be used to manipulate the
appearance.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>float <i class="arg">xdata</i></dt>
<dd><p>- Series of independent data</p></dd>
<dt>float <i class="arg">ydata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="122"><b class="cmd">::math::statistics::plot-xyline</b> <i class="arg">canvas</i> <i class="arg">xdata</i> <i class="arg">ydata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a line through the data points. The tag can be used to
manipulate the appearance.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">xdata</i></dt>
<dd><p>- Series of independent data</p></dd>
<dt>list <i class="arg">ydata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="123"><b class="cmd">::math::statistics::plot-tdata</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a collection of dots. The horizontal coordinate is equal to the
index. The tag can be used to manipulate the appearance.
This type of presentation is suitable for autocorrelation functions for
instance or for inspecting the time-dependent behaviour.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">tdata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="124"><b class="cmd">::math::statistics::plot-tline</b> <i class="arg">canvas</i> <i class="arg">tdata</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple XY plot in the given canvas - the data are
shown as a line. See plot-tdata for an explanation.</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">tdata</i></dt>
<dd><p>- Series of dependent data</p></dd>
<dt>string <i class="arg">tag</i></dt>
<dd><p>- Tag to give to the plotted data (defaults to xyplot)</p></dd>
</dl></dd>
<dt><a name="125"><b class="cmd">::math::statistics::plot-histogram</b> <i class="arg">canvas</i> <i class="arg">counts</i> <i class="arg">limits</i> <i class="arg">tag</i></a></dt>
<dd><p>Create a simple histogram in the given canvas</p>
<dl class="doctools_arguments">
<dt>widget <i class="arg">canvas</i></dt>
<dd><p>- Canvas widget to use</p></dd>
<dt>list <i class="arg">counts</i></dt>
<dd><p>- Series of bucket counts</p></dd>
<dt>list <i class="arg">limits</i></dt>

&#124; <a href="../../../toc.html">Table Of Contents</a>
&#124; <a href="../../../../index.html">Keyword Index</a>
&#124; <a href="../../../../toc0.html">Categories</a>
&#124; <a href="../../../../toc1.html">Modules</a>
&#124; <a href="../../../../toc2.html">Applications</a>
 ] <hr>
<div class="doctools">
<h1 class="doctools_title">practcl(n) 0.16.4 tcllib &quot;The The Proper Rational API for C to Tool Command Language Module&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>practcl - The Practcl Module</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>

<dt><a name="15">proc <b class="cmd">practcl::mkzip</b> <i class="arg">exename</i> <i class="arg">barekit</i> <i class="arg">vfspath</i></a></dt>
<dd><p>Build a zipfile. On tcl8.6 this invokes the native Zip implementation
 on older interpreters this invokes zip via exec</p></dd>
<dt><a name="16">proc <b class="cmd">practcl::sort_dict</b> <i class="arg">list</i></a></dt>
<dd><p>Dictionary sort a key/value list. Needed because pre tcl8.6
 does not have <em>lsort -stride 2</em></p></dd>
<dt><a name="17">proc <b class="cmd">practcl::local_os</b></a></dt>
<dd><p>Returns a dictionary describing the local operating system.
 Fields return include:</p>
<ul class="doctools_itemized">
 
<li><p>download - Filesystem path where fossil repositories and source tarballs are downloaded for the current user</p></li>
<li><p>EXEEXT - The extension to give to executables. (i.e. .exe on windows)</p></li>
<li><p>fossil_mirror - A URI for a local network web server who acts as a fossil repository mirror</p></li>
<li><p>local_install - Filesystem path where packages for local consumption by the current user are installed</p></li>
<li><p>prefix - The prefix as given to the Tcl core/TEA for installation to local_install in ./configure</p></li>
<li><p>sandbox - The file location where this project unpacks external projects</p></li>
<li><p>TEACUP_PROFILE - The ActiveState/Teacup canonical name for this platform (i.e. win32-ix86 macosx10.5-i386-x86_84)</p></li>
<li><p>TEACUP_OS - The local operating system (windows, macosx, openbsd, etc). Gives the same answer as tcl.m4, except that macosx is given as macosx instead of Darwin.</p></li>
<li><p>TEA_PLATFORM - The platform returned by uname -s-uname -r (on Unix), or &quot;windows&quot; on Windows</p></li>
<li><p>TEACUP_ARCH - The processor architecture for the local os (i.e. ix86, x86_64)</p></li>
<li><p>TEACUP_ARCH - The processor architecture for the local os (i.e. ix86, x86_64)</p></li>
<li><p>teapot - Filesystem path where teapot package files are downloaded for the current user</p></li>
<li><p>userhome - File path to store localized preferences, cache download files, etc for the current user</p></li>
</ul>
<p>This command uses a combination of local checks with Exec, any tclConfig.sh file that is
 resident, autoconf data where already computed, and data gleaned from a file named
 practcl.rc in userhome. The location for userhome varies by platform and operating system:</p>
<ul class="doctools_itemized">
 
<li><p>Windows: ::env(LOCALAPPDATA)/Tcl</p></li>
<li><p>Macos: ~/Library/Application Support/Tcl</p></li>
<li><p>Other: ~/tcl</p></li>
</ul></dd>
<dt><a name="18">proc <b class="cmd">practcl::config.tcl</b> <i class="arg">path</i></a></dt>
<dd><p>A transparent call to ::practcl::read_configuration to preserve backward compadibility
 with older copies of Practcl</p></dd>
<dt><a name="19">proc <b class="cmd">practcl::read_configuration</b> <i class="arg">path</i></a></dt>
<dd><p>Detect local platform. This command looks for data gleaned by autoconf or autosetup
 in the path specified, or perform its own logic tests if neither has been run.
 A file named config.site present in the location indicates that this project is
 cross compiling, and the data stored in that file is used for the compiler and linker.</p>
<p>This command looks for information from the following files, in the following order:</p>
<ul class="doctools_itemized">
 
<li><p>config.tcl - A file generated by autoconf/configure in newer editions of TEA, encoded as a Tcl script.</p></li>
<li><p>config.site - A file containing cross compiler information, encoded as a SH script</p></li>
<li><p>::env(VisualStudioVersion) - On Windows, and environmental value that indicates MS Visual Studio is installed</p></li>
</ul>
<p>This command returns a dictionary containing all of the data cleaned from the sources above.
 In the absence of any guidance this command returns the same output as ::practcl::local_os.
 In this mode, if the environmental variable VisualStudioVersion exists, this command
 will provide a template of fields that are appropriate for compiling on Windows under
 Microsoft Visual Studio. The USEMSVC flag in the dictionary is a boolean flag to indicate
 if this is indeed the case.</p></dd>
<dt><a name="20">proc <b class="cmd">practcl::tcllib_require</b> <i class="arg">pkg</i> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Try to load  a package, and failing that
 retrieve tcllib</p></dd>
<dt><a name="21">proc <b class="cmd">practcl::platform::tcl_core_options</b> <i class="arg">os</i></a></dt>
<dd><p>Return the string to pass to ./configure to compile the Tcl core for the given OS.</p>
<ul class="doctools_itemized">
 
<li><p>windows: --with-tzdata --with-encoding utf-8</p></li>
<li><p>macosx: --enable-corefoundation=yes  --enable-framework=no --with-tzdata --with-encoding utf-8</p></li>
<li><p>other: --with-tzdata --with-encoding utf-8</p></li>
</ul></dd>
<dt><a name="22">proc <b class="cmd">practcl::platform::tk_core_options</b> <i class="arg">os</i></a></dt>
<dd></dd>
<dt><a name="23">proc <b class="cmd">practcl::read_rc_file</b> <i class="arg">filename</i> <span class="opt">?<i class="arg">localdat</i> <b class="const"></b>?</span></a></dt>
<dd><p>Read a stylized key/value list stored in a file</p></dd>
<dt><a name="24">proc <b class="cmd">practcl::read_sh_subst</b> <i class="arg">line</i> <i class="arg">info</i></a></dt>
<dd><p>Converts a XXX.sh file into a series of Tcl variables</p></dd>
<dt><a name="25">proc <b class="cmd">practcl::read_sh_file</b> <i class="arg">filename</i> <span class="opt">?<i class="arg">localdat</i> <b class="const"></b>?</span></a></dt>

<dd><p>Delete the contents of <em>d2</em>, and then
 recusively Ccopy the contents of <em>d1</em> to <em>d2</em>.</p></dd>
<dt><a name="42">proc <b class="cmd">practcl::copyDir</b> <i class="arg">d1</i> <i class="arg">d2</i> <span class="opt">?<i class="arg">toplevel</i> <b class="const">1</b>?</span></a></dt>
<dd><p>Recursively copy the contents of <em>d1</em> to <em>d2</em></p></dd>
<dt><a name="43">proc <b class="cmd">practcl::buildModule</b> <i class="arg">modpath</i></a></dt>
<dd></dd>
<dt><a name="44">proc <b class="cmd">practcl::installModule</b> <i class="arg">modpath</i> <i class="arg">DEST</i></a></dt>
<dd><p>Install a module from MODPATH to the directory specified.
 <em>dpath</em> is assumed to be the fully qualified path where module is to be placed.
 Any existing files will be deleted at that path.
 If the path is symlink the process will return with no error and no action.
 If the module has contents in the build/ directory that are newer than the
 .tcl files in the module source directory, and a build/build.tcl file exists,
 the build/build.tcl file is run.
 If the source directory includes a file named index.tcl, the directory is assumed
 to be in the tao style of modules, and the entire directory (and all subdirectories)
 are copied verbatim.
 If no index.tcl file is present, all .tcl files are copied from the module source
 directory, and a pkgIndex.tcl file is generated if non yet exists.
 I a folder named htdocs exists in the source directory, that directory is copied
 verbatim to the destination.</p></dd>
<dt><a name="45">proc <b class="cmd">practcl::trigger</b> <span class="opt">?<i class="arg">args</i>?</span></a></dt>
<dd><p>Trigger build targets, and recompute dependencies</p>
<p>Internals:</p>
<pre class="doctools_example">
  ::practcl::LOCAL make trigger {*}$args
  foreach {name obj} [::practcl::LOCAL make objects] {
    set ::make($name) [$obj do]

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<h1 class="doctools_title">profiler(n) 0.5 tcllib &quot;Tcl Profiler&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>profiler - Tcl source code profiler</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">COMMANDS</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.3</b></li>
<li>package require <b class="pkgname">profiler <span class="opt">?0.5?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::profiler::init</b></a></li>
<li><a href="#2"><b class="cmd">::profiler::dump</b> <i class="arg">pattern</i></a></li>
<li><a href="#3"><b class="cmd">::profiler::print</b> <span class="opt">?<i class="arg">pattern</i>?</span></a></li>
<li><a href="#4"><b class="cmd">::profiler::reset</b> <span class="opt">?<i class="arg">pattern</i>?</span></a></li>
<li><a href="#5"><b class="cmd">::profiler::suspend</b> <span class="opt">?<i class="arg">pattern</i>?</span></a></li>
<li><a href="#6"><b class="cmd">::profiler::resume</b> <span class="opt">?<i class="arg">pattern</i>?</span></a></li>
<li><a href="#7"><b class="cmd">::profiler::new-disabled</b></a></li>
<li><a href="#8"><b class="cmd">::profiler::new-enabled</b></a></li>
<li><a href="#9"><b class="cmd">::profiler::sortFunctions</b> <i class="arg">key</i></a></li>
</ul>
</div>
</div>
<div id="section1" class="doctools_section"><h2><a name="section1">Description</a></h2>
<p>The <b class="package">profiler</b> package provides a simple Tcl source code
profiler.  It is a function-level profiler; that is, it collects only
function-level information, not the more detailed line-level

has been gathered previously.  Use resume command to re-enable
profiling.</p></dd>
<dt><a name="6"><b class="cmd">::profiler::resume</b> <span class="opt">?<i class="arg">pattern</i>?</span></a></dt>
<dd><p>Resume profiling for all functions matching <i class="arg">pattern</i>.  If no
pattern is specified, profiling will be resumed for all functions.
This command should be invoked after suspending the profiler in the
code.</p></dd>
<dt><a name="7"><b class="cmd">::profiler::new-disabled</b></a></dt>
<dd><p>Change the initial profiling state for new procedures. Invoking this
command disables profiling for all procedures created after this
command until <b class="cmd">new-enabled</b> is invoked. Activate profiling of
specific procedures via <b class="cmd">resume</b>.</p></dd>
<dt><a name="8"><b class="cmd">::profiler::new-enabled</b></a></dt>
<dd><p>Change the initial profiling state for new procedures. Invoking this
command enables profiling for all procedures created after this
command until <b class="cmd">new-disabled</b> is invoked. Prevent profiling of
specific procedures via <b class="cmd">suspend</b>.</p></dd>
<dt><a name="9"><b class="cmd">::profiler::sortFunctions</b> <i class="arg">key</i></a></dt>
<dd><p>Return a list of functions sorted by a particular profiling statistic.
Supported values for <i class="arg">key</i> are: <b class="const">calls</b>,
<b class="const">exclusiveTime</b>, <b class="const">compileTime</b>, <b class="const">nonCompileTime</b>,
<b class="const">totalRuntime</b>, <b class="const">avgExclusiveTime</b>, and
<b class="const">avgRuntime</b>.  The return result is a list of lists, where each
sublist consists of a function name and the value of <i class="arg">key</i> for
that function.</p></dd>

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<h1 class="doctools_title">struct::matrix(n) 2.0.4 tcllib &quot;Tcl Data Structures&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>struct::matrix - Create and manipulate matrix objects</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">EXAMPLES</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.2</b></li>
<li>package require <b class="pkgname">struct::matrix <span class="opt">?2.0.4?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">::struct::matrix</b> <span class="opt">?<i class="arg">matrixName</i>?</span> <span class="opt">?<b class="const">=</b>|<b class="const">:=</b>|<b class="const">as</b>|<b class="const">deserialize</b> <i class="arg">source</i>?</span></a></li>
<li><a href="#2"><b class="cmd">matrixName</b> <i class="arg">option</i> <span class="opt">?<i class="arg">arg arg ...</i>?</span></a></li>
<li><a href="#3"><i class="arg">matrixName</i> <b class="method">=</b> <i class="arg">sourcematrix</i></a></li>
<li><a href="#4"><i class="arg">matrixName</i> <b class="method">--&gt;</b> <i class="arg">destmatrix</i></a></li>
<li><a href="#5"><i class="arg">matrixName</i> <b class="method">add column</b> <span class="opt">?<i class="arg">values</i>?</span></a></li>

<div id="keywords" class="doctools_section"><h2><a name="keywords">Keywords</a></h2>
<p><a href="../../../../index.html#matrix">matrix</a></p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Data structures</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 2002-2013,2019 Andreas Kupries &lt;[email protected]&gt;</p>
</div>
</div></body></html>

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<div class="doctools">
<h1 class="doctools_title">struct::matrix_v1(n) 1.2.2 tcllib &quot;Tcl Data Structures&quot;</h1>
<div id="name" class="doctools_section"><h2><a name="name">Name</a></h2>
<p>struct::matrix_v1 - Create and manipulate matrix objects</p>
</div>
<div id="toc" class="doctools_section"><h2><a name="toc">Table Of Contents</a></h2>
<ul class="doctools_toc">
<li class="doctools_section"><a href="#toc">Table Of Contents</a></li>
<li class="doctools_section"><a href="#synopsis">Synopsis</a></li>
<li class="doctools_section"><a href="#section1">Description</a></li>
<li class="doctools_section"><a href="#section2">EXAMPLES</a></li>
<li class="doctools_section"><a href="#section3">Bugs, Ideas, Feedback</a></li>
<li class="doctools_section"><a href="#keywords">Keywords</a></li>
<li class="doctools_section"><a href="#category">Category</a></li>
<li class="doctools_section"><a href="#copyright">Copyright</a></li>
</ul>
</div>
<div id="synopsis" class="doctools_section"><h2><a name="synopsis">Synopsis</a></h2>
<div class="doctools_synopsis">
<ul class="doctools_requirements">
<li>package require <b class="pkgname">Tcl 8.2</b></li>
<li>package require <b class="pkgname">struct::matrix <span class="opt">?1.2.2?</span></b></li>
</ul>
<ul class="doctools_syntax">
<li><a href="#1"><b class="cmd">matrixName</b> <i class="arg">option</i> <span class="opt">?<i class="arg">arg arg ...</i>?</span></a></li>
<li><a href="#2"><i class="arg">matrixName</i> <b class="method">add column</b> <span class="opt">?<i class="arg">values</i>?</span></a></li>
<li><a href="#3"><i class="arg">matrixName</i> <b class="method">add row</b> <span class="opt">?<i class="arg">values</i>?</span></a></li>
<li><a href="#4"><i class="arg">matrixName</i> <b class="method">add columns</b> <i class="arg">n</i></a></li>
<li><a href="#5"><i class="arg">matrixName</i> <b class="method">add rows</b> <i class="arg">n</i></a></li>

<div id="keywords" class="doctools_section"><h2><a name="keywords">Keywords</a></h2>
<p><a href="../../../../index.html#matrix">matrix</a></p>
</div>
<div id="category" class="doctools_section"><h2><a name="category">Category</a></h2>
<p>Data structures</p>
</div>
<div id="copyright" class="doctools_section"><h2><a name="copyright">Copyright</a></h2>
<p>Copyright &copy; 2002,2019 Andreas Kupries &lt;[email protected]&gt;</p>
</div>
</div></body></html>